Patent Publication Number: US-2010119993-A1

Title: Dental implant

Description:
FIELD OF THE INVENTION 
     This invention relates to dental implants. 
     BACKGROUND OF THE INVENTION 
     Dental implants are used as replacements for missing teeth. Implants are typically in the form of a fixture that is coupled to an abutment. The fixture portion of a dental implant is that portion which extends into the maxilla or mandible, where it is anchored in a bone in the maxilla or mandible. The fixture typically includes a top portion that extends out of the maxilla or mandible and provides an anchoring point for an abutment. The abutment portion of a dental implant is the portion that is fixed to the fixture and extends above the gingiva. It has an upper surface that is configured to receive and support a crown. 
     There are several common problems with such two piece dental implants. First, the bone into which they are inserted often does not bond (e.g. integrate) well with the implant, or, if bonded, degrades causing the implant to loosen over time. 
     Microgaps between the fixture and the abutment are one cause of this loss of bone. The fixture is often positioned within the maxilla or mandible such that its upper surface is below the gingiva. When an abutment is fixed to the fixture, there is a tiny gap between the abutment and the fixture that is at least partially disposed beneath the gingiva. This microgap becomes a haven or reservoir for oral bacteria. By cultivating oral bacteria so close to the fixture/bone junction itself, the gingiva may become irritated or infected, and the bond between the fixture and the maxilla or mandible weakened. 
     Loosening may also be caused by the poor distribution of forces from the implant to the maxilla or mandible. If the load is concentrated on a particular portion of the maxilla or mandible, this stress concentration may cause the bond between fixture and maxilla or mandible to weaken. Stress concentrations are typically caused by improper fixture design or positioning, or a fixture that is not shaped to distribute the tooth load relatively evenly. 
     Teeth are naturally designed to resist stress of chewing by their root shape, position and coronal contours. An implant that would closely simulate these same root and coronal contours and would best be surgically placed in the position of the natural tooth, should be the best design to prevent the noted clinical problems in implant dentistry. This new design would allow the bone and tissue contours to appear normal and prevent the loss of bone and tissue contours seen with the current implant systems. An enhanced esthetic and functional outcome could be realized by appropriately defining the shape, contours and position of a new implant design. 
     At times there are many or all of the teeth missing. Teeth work in harmony with each other by distributing chewing forces, by contouring the bone and tissue by their shape and outline form and by creating a mutually protected biological environment. When multiple teeth are lost, it compounds the mentioned problems. As the bone heals to the implant, it assumes the contour of the implant. If it is round, it will heal to a round shape, thus remodeling the bone to the shape of the implant. This remodeling is the main cause for loss of bone and tissue contours and implant stability. If we surgically place a number of adjacent implants, the bone remodeling is magnified because we have lost the adjacent teeth which helps keep the contours of the bone. Therefore, a implant system that individually and mutually helps to maintain the normal contours of the bone would be beneficial. This system of implants may have individual contours for each teeth that are replaced and as a group are beneficially related to each other in orientation. The system of implants should be positioned correctly from a mesial-distal, a facial-lingual and from an incisal/occlusal-cervical and have root contours similar to teeth. This new system will function to restore and maintain bone contours, stabilize the implant during chewing and restore esthetic tissue contours to the implants replacing the missing teeth. This new system would give the best opportunity to regain the normal biological response of natural teeth. 
     Another problem often encountered with implants is the failure of the crown that is attached to the abutment. Large loads placed on the crown when chewing cause the crown to fatigue and ultimately to fracture or fail. These large loads can also weaken the cement that bonds the crown to the abutment if the crown-to-abutment joint design unduly concentrates the load. Current abutment designs are shaped in a similar shape as the connecting fixture. If the fixture is round, the abutment is round with flat sides. In preparing a tooth for a crown a specific outline form of the preparation helps to distribute forces with proper retention and resistance form. Similarly an implant abutment should follow similar principles in creating proper outline forms for resistance and retention. 
     SUMMARY OF THE INVENTION 
     In accordance with a first aspect of the invention, an oral implant for mounting in a patient&#39;s maxilla or mandible is provided, including an abutment having a longitudinal axis, the abutment having a first portion extending upward from a junction line and a second portion extending downward from the junction line; wherein the junction line defines the intersection between the first and second portions and extends circumferentially about the entire periphery of the abutment; wherein the first portion has a surface that extends about the entire periphery of the abutment, said surface terminating at the junction line, said surface further tapering inwardly in a direction extending upwardly from the junction line; and wherein the second portion has a surface that extends about the entire periphery of the abutment, said surface terminating at the junction line, said surface further tapering inwardly in a direction extending downwardly from the junction line; and a fixture having a longitudinal axis, the fixture being configured to be embedded in the patient&#39;s maxilla or mandible; wherein the fixture has a top surface with an aperture therein, said aperture extending downwardly into the fixture and tapering inwardly in a direction extending downwardly into the fixture. 
     The surface of the first portion of the abutment may taper inwardly at an angle of between 0.5 and 10 degrees with respect to the longitudinal axis and wherein the surface of the second portion of the abutment tapers inwardly at an angle of between 0.5 and 20 degrees with respect to the longitudinal axis. An inward angle of taper of both a mesial and a distal side of the first portion with respect to the longitudinal axis of the abutment may be between 0.5 and 6 degrees. An inward angle of taper of a lingual side of the first portion with respect to the longitudinal axis of the abutment may be between 6 and 8 degrees. An inward angle of taper of a facial side of the first portion with respect to the longitudinal axis of the abutment is between 6 and 8 degrees. An inward angle of taper of a facial side of the second portion with respect to the longitudinal axis of the abutment may be between 10 and 20 degrees. An inward angle of taper of a lingual side of the second portion with respect to the longitudinal axis of the abutment may be between 10 and 20 degrees. An inward angle of taper of both a mesial and a distal side of the second portion with respect to the longitudinal axis of the abutment may be between 0.5 and 10 degrees. The junction line may be higher on both the mesial side and the distal side than it is on both the lingual and facial sides. The top edge of the aperture may be between 0.0 and 1.5 mm from the junction line around substantially all the periphery of the abutment. The top surface of the fixture may extend laterally outward from the abutment a relatively constant distance of between 0.5 and 1.5 mm about the complete periphery of the fixture. The abutment may define a through hole extending through the abutment with a longitudinal axis coaxial with the longitudinal axis of the abutment. The through hole may have an internal shoulder axially disposed above a minima of the junction line and below a maxima of the junction line, wherein a threaded aperture is disposed at the bottom of the aperture in the fixture, and further wherein the implant further comprises a threaded fastener having a head abutting the shoulder and a threaded portion threaded into the threaded aperture. The second portion of the abutment may have a first plurality of nodes and the first portion of the abutment may have a second plurality of nodes and further wherein the first plurality of nodes may be aligned with the second plurality of nodes at the junction line. The first portion of the abutment may have a generally elliptical axial cross section and the second portion of the abutment may have a generally elliptical axial cross section. The major axes of the generally elliptical cross sections of both the first and second portions may extend in a lingual-facial direction. The junction line may have peaks disposed at the mesial and distal sides of the abutment and valleys disposed at the lingual and facial sides of the abutment. An angle between the first portion and the second portion on both a mesial and a distal side of the abutment may be between 115 and 180 degrees, and the angle may lie in a plane that includes the longitudinal axis. An angle between the first portion and the second portion on the lingual side of the abutment may be between 135 and 170 degrees, and the angle may lie in a plane that includes the longitudinal axis. An angle between the first portion and the second portion on the facial side of the abutment may be between 135 and 175 degrees, and the angle may lie in a plane that includes the longitudinal axis. The fixture may have a lower portion configured to be received in an osteotomy to a first depth, the lower portion defining at least one longitudinal groove extending substantially the entire length of the lower portion. The abutment may define a facial plane extending from the top of the abutment down a facial side of the abutment. The abutment may define a lingual plane extending from the top of the abutment down a lingual side of the abutment. The aperture of the fixture may have a bottom, and a threaded aperture may extend longitudinally into the bottom of the aperture, and the threaded aperture may have a flat bottom. The fixture may be threaded on its outer surface, having threads extending upward, said threads having an upper terminus below the flat bottom of the threaded aperture. A top surface of the fixture may define at least one maximum and at least one minimum, and a hole extending through the abutment may have an internal shoulder axially disposed above the at least one minimum of the top surface and below the at least one maximum of the top surface. 
     In accordance with a second aspect of the invention, a system of implants for implantation into a maxilla in a plurality of tooth apertures previously occupied by natural teeth is provided, the system including a first implant having a fixture with an upper surface defining a first mesial maximum, a first distal maximum, a first facial minimum, and a first lingual minimum; a second implant having a fixture with an upper surface defining a second mesial maximum, a second distal maximum, a second facial minimum, and a second lingual minimum; wherein the first implant is configured to be disposed in a first tooth aperture, wherein the second implant is configured to be disposed in a second tooth aperture, wherein the first tooth aperture is immediately adjacent to and mesial to the second tooth aperture, and further wherein the first and second implants are configured to be held in predetermined relative positions with respect to each other within their respective apertures when they are fixed in a maxilla. 
     The first implant may be configured to be received in a central incisor aperture, and the second implant may be configured to be received in a lateral incisor aperture when the first and second implants are in said predetermined relative positions. The first distal maximum may be higher than the second mesial maximum when the first and second implants are in said predetermined relative positions. The overall width in a facial-lingual direction of the first implant may be greater than the overall width in a facial-lingual direction of the second implant when the first and second implants are in said predetermined relative positions. The first implant may extend farther forward in a facial direction than the second implant when the first and second implants are in said predetermined relative positions. The overall width in a mesial-distal direction of the first implant may be greater than the overall width in a mesial-distal direction of the second implant when the first and second implants are in said predetermined relative positions. The first implant may extend farther in a lingual direction than the second implant when the first and second implants are in said predetermined relative positions. The first implant may be configured to be received in a lateral incisor aperture, and the second implant may be configured to be received in a cuspid aperture when the first and second implants are in said predetermined relative positions. The first distal maximum may be lower than the second mesial maximum when the first and second implants are in said predetermined relative positions. The overall width in a facial-lingual direction of the first implant may be less than the overall width in a facial-lingual direction of the second implant when the first and second implants are in said predetermined relative positions. The second implant may extend farther forward in a facial direction than the first implant when the first and second implants are in said predetermined relative positions. The overall width in a mesial-distal direction of the first implant may be less than the overall width in a mesial-distal direction of the second implant when the first and second implants are in said predetermined relative positions. The second implant may extend farther in a lingual direction than the first implant when the first and second implants are in said predetermined relative positions. An overall width of the first implant in the facial-lingual direction may be greater than an overall width of the first implant in the mesial-distal direction, and an overall width of the second implant in the facial-lingual direction may be greater than an overall width of the second implant in the mesial-distal direction when the first and second implants are in said predetermined relative positions. 
     In accordance to a third aspect of the invention, a system of implants for implantation into a maxilla in a plurality of tooth apertures previously occupied by natural teeth is provided, the system including a first implant having a fixture with an upper surface defining two first maxima, said first maxima being disposed on opposite sides of the implant along a mesial/distal axis, a first facial minimum and a second lingual minimum; a second implant having a fixture with an upper surface defining two second maxima, the second maxima being disposed on opposite sides of the implant along a mesial/distal axis, a second facial minimum, and a second lingual minimum; wherein the first implant is configured to be disposed in a first tooth aperture, wherein the second implant is configured to be disposed in a second tooth aperture, wherein the first tooth aperture is immediately adjacent to the second tooth aperture, and wherein the first and second implants are configured to be held in predetermined relative positions with respect to each other within their respective apertures when they are fixed in a maxilla. 
     The first implant may be configured to be received in a left central incisor aperture, and the second implant may be configured to be received in a right central incisor aperture when the first and second implants are in said predetermined relative positions. One of the first maxima may be adjacent to one of the second maxima and the two adjacent maxima may be at the same height when the first and second implants are in said predetermined relative positions. The overall width in a facial-lingual direction of the first implant may be the same as the overall width in a facial-lingual direction of the second implant when the first and second implants are in said predetermined relative positions. The first implant may extend the same distance forward in a facial direction as the second implant when the first and second implants are in said predetermined relative positions. The overall width in a mesial-distal direction of the first implant may be the same as the overall width in a mesial-distal direction of the second implant when the first and second implants are in said predetermined relative positions. The first implant may extend the same distance in a lingual direction as the second implant when the first and second implants are in said predetermined relative positions. Another of the first maxima and another of the second maxima may be disposed at different heights from said adjacent ones of said first maxima. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1-7  are perspective, top, right-side, front, left-side, rear and bottom views of a unitary right central mandibular incisor implant. 
         FIGS. 8-14  are perspective, top, right-side, front, left-side, rear and bottom views of a unitary right lateral maxillar incisor implant. 
         FIG. 15  is a cross-section of both of the implants of  FIGS. 1-14  at any of cross-sections A-A, B-B, and C-C. 
         FIG. 16  is an alternative cross-section of any of the implants of  FIGS. 1-14  showing a faceted outer surface and taking at sections A-A, B-B, and C-C. 
         FIG. 17  is a cross-section of either of the implants of  FIGS. 1-14  taken at section line D-D. 
         FIG. 18  is a cross-section of any of the implants of  FIGS. 1-14  taken at section line E-E. 
         FIG. 19A  is a fragmentary front view of any of the implants of the foregoing figures showing how the flare angle measured at the sides of the implant increases as one travels upward along the shaft of the implant. 
         FIG. 19B  similarly illustrates how the flare angle increases as one travels upward along the implant as measured on the front side of the implant. 
         FIG. 20  is a top view of any of the foregoing implants illustrating the narrow band having a Width that extends circumferentially around the entire implant. 
         FIG. 21  is a fragmentary rear view of any of the foregoing implants showing a local minima (low point) of the narrow band extending around the implant that is located on the center of the back side of the implant. 
         FIG. 22  is a fragmentary side view of any of the foregoing implants showing the local minima at the rear of the implant and a slightly higher local minima at the front of the implant, as well as the two imaginary planes  142  and  144  that define the front portion and rear portion of the narrow band. 
         FIG. 23  is a fragmentary front view of any of the foregoing implants showing the local minima at the front center of the implant. 
         FIG. 24  is a top view of any of the foregoing implants showing the numeral 3-node configuration of both the lower portion of the implant and the upper portion of the implant and also illustrating how each of the three (3) nodes of the upper portion of the implant are disposed immediately adjacent to each of the three (3) nodes of the lower portion of the implant. 
         FIGS. 25A-25D  illustrate top, side, rear and bottom views of an alternative upper abutment portion of the implant that can be employed together with an alternative form of the lower portion of the implant shown in  FIGS. 26A-26C . 
         FIGS. 26A-26C  are top, side, and rear views of an alternative lower portion of the implant that may be coupled together with the upper portion shown in  FIGS. 25A-25D  to form a two-piece implant having the identical structure, configuration, arrangement, dimensions, features, and capabilities as the implants described in the foregoing FIGURES with one (1) difference: the implant is made of two pieces coupled together by a cylinder extending downward from the upper portion in  FIGS. 25A-25C  into the cylindrical recess shown in  FIGS. 26A-26C . 
         FIG. 26D  is a partial cross-sectional left side view of the implant formed by coupling the implant upper portion or abutment of  FIG. 25A-25D  and the implant lower portion illustrated in  FIGS. 26A-26C  in which a cylindrical portion of the upper portion extending downward therefrom is received in a matching cylindrical hole in the top of the lower portion shown in  FIGS. 26A-26C  held together by a screw recessed into the top of the upper portion, extending through the upper portion, and threadedly engaged with mating internal threads disposed in the upper part of the lower portion of the implant. 
         FIG. 27  is an alternative cross-sectional profile of the cylinder of the upper portion of the implants in  FIGS. 25A-25D  and the cylindrical hole in the lower portion of the implant shown in  FIGS. 26A-26C  illustrating a triangular sharp-edged protrusion that extends the length of the cylinder in place of the existing protrusion  214  and corresponding recess or slot  190 . 
         FIG. 28  illustrates an alternative cross-section of the cylinder and cylindrical hole of the foregoing figures showing the protrusion and recess as a three-sided trapezoidal shape. 
         FIG. 29  is yet another alternative profile of the cylinder and cylindrical recess of foregoing figures showing the protrusion and slot as a rectangular (for example square) shape extending outward from the cylinder. 
         FIG. 30  illustrates an alternative profile of the cylinder and cylindrical hole in the foregoing figures in which the protrusion and recess of those figures has been removed and the cylinder (and cylindrical hole) faceted with longitudinally extending facets that extend the length of the cylinder and cylindrical hole. Facets shall mean flat planar surfaces. 
         FIG. 31  is an alternative profile of the cylinder and cylindrical hole in the foregoing figures showing the position of the protrusion and the slot reversed: the cylinder extending downward from the upper portion of the implant has a hemispherical slot and the cylindrical hole in the lower portion of the implant has an inwardly extending hemispherical protrusion. 
         FIGS. 32-45  illustrate the upper portion and the lower portion of a two-piece implant intended to be used in place of an upper cuspid having the same mating construction as that described above with regard to  FIGS. 25-31  wherein  FIGS. 32-38  are perspective, top, right-side, front, left-side, rear, and bottom views of the upper portion of the implant and  FIGS. 39-45  are perspective, top, right-side, front, left-side, rear, and bottom views of the lower portion into which the upper portion is inserted. 
         FIGS. 46-59  illustrate the upper and lower portion of a two-piece implant intended for use as a lower cuspid in which  FIGS. 46-52  are perspective, top, right-side, front, left-side, rear, and bottom views of the upper portion of the implant and further wherein  FIGS. 53-59  are perspective, top, right-side, front, left-side, rear and bottom views of the lower portion of the implant. 
         FIGS. 60-73  illustrate the upper and lower portions of a two-piece implant intended for use as a first lower pre-molar, wherein  FIGS. 60-66  are perspective, top, right-side, front, left-side, rear and bottom views of the upper portion of the implant and  FIGS. 67-73  are perspective, top, right-side, front, left-side, rear and bottom views of the lower portion of the implant. 
         FIGS. 74-87  illustrate an alternative two-piece implant intended for use as a first upper pre-molar implant, in which  FIGS. 74-80  illustrate perspective, top, right-side, front, left-side, rear and bottom views of the upper portion of the implant and  FIGS. 81-87  illustrate perspective, top, right-side, front, left-side, rear, and bottom views of the lower portion of the implant. 
         FIGS. 88-101  illustrate the upper and lower portions of a two-piece implant intended to replace a lower molar, in which  FIGS. 88-94  illustrate perspective, top, right-side, front, left-side, rear, and bottom views of the upper portion of the implant and  FIGS. 95-101  illustrate perspective, top, right-side, front, left-side, rear, and bottom views of the lower portion of the implant. 
         FIGS. 102-115  illustrate an alternative two-piece implant intended to be used as an upper molar, wherein  FIGS. 102-108  are perspective, top, right-side, front, left-side, rear, and bottom views of the upper portion of the implant and  FIGS. 109-115  illustrate perspective, top, right-side, front, left-side, rear and bottom views of the lower portion of the implant. 
         FIGS. 116-130  illustrate an abutment and fixture of an alternative two-piece implant configured for use to replace a lateral # 7  incisor. An identical but mirror image two-piece implant (not illustrated) is configured for use to replace a lateral #10 incisor. 
         FIGS. 131-146  illustrate an abutment and fixture of an alternative two-piece implant configured for use to replace a central #8 incisor. An identical but mirror image two-piece implant (not illustrated) is configured for use to replace a central #9 incisor. 
         FIGS. 147-162  illustrate an abutment and fixture of an alternative two-piece implant configured for use to replace a #6 cuspid. And identical but mirror image two-piece implant (not illustrated) is configured for use to replace a #11 cuspid. 
         FIGS. 163-164  are left side cross-sectional and rear views (respectively) of the two piece implant of  FIGS. 116-130  in assembled form with a fastener holding the components together. 
         FIGS. 165-166  are left side cross-sectional and rear views (respectively) of the two piece implant of  FIGS. 131-146  in assembled form with a fastener holding the components together. 
         FIGS. 167-168  are left side cross-sectional and rear views (respectively) of the two piece implant of  FIGS. 147-162  in assembled form with a fastener holding the components together. 
         FIGS. 169-171  are facial, bottom and lingual views, respectively, of a fragmentary portion of a maxilla with a plurality of implants in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the discussion below, the applicants describe a dental implant that is inserted into prepared holes in a mandible or maxilla. To describe several features of the implant, the Applicants use several terms that are here defined or described. 
     “Up” used herein with reference to teeth, implants, fixtures, or abutments, refers to the direction generally parallel to the longitudinal axis of the implant or tooth and extending away from the bone in which it is intended to be implanted (i.e. away from the root and toward the crown). 
     “Down” is the direction opposite to “up” (i.e. away from the crown and toward the root). 
     A “side”, as used with reference to teeth, implants, fixtures, or abutments, refers to the portions of the tooth or implant facing the adjacent teeth or implants when the tooth, implant, fixture, or abutment is embedded in the mandible or maxilla. The side surfaces of teeth or implants directly face the adjacent teeth or implants. 
     A “side” can be either “mesial” or “distal” depending upon whether the side faces toward the dental mid-line or away from the dental mid-line, respectively. 
     “Front” when used with reference to a tooth, implant, fixture, or abutment refers to the portion that faces outward away from the maxilla or mandible and may also be referred to as “facial” or “buccal”. 
     “Rear” when used with reference to a tooth, implant, fixture, or abutment refers to the portion that faces the inside of the mouth and may also be referred to as “lingual”. 
     The term “CEJ” or “cement-enamel junction”, is the line on a tooth defined by the junction of the enameled upper portion and the cementum of the root. It extends around the surface of the tooth generally perpendicular to the longitudinal axis of the tooth and is generally oval in shape. Since the upper portion of a tooth is covered with enamel, the CEJ typically extends around the outer surface of the tooth at the lowest extent of the enamel. If the tooth is eroded, however, the cementum and enamel may not be in contact and therefore the location of the CEJ may be unclear. 
     The term “CRJ” or “coronal-root junction” refers to the junction between the coronal portion and the root portion of a tooth. It extends around each tooth in a generally oval shape, and is a little higher on the sides of the tooth than on the front or back of the tooth. 
     A “facial CRJ line” (also “frontal CRJ line”) refers to an imaginary line extending across the face of a mandible or maxilla that passes through the front and lowermost portion of the CRJ of each tooth or implant in the mandible or maxilla. Since the mandible and maxilla each have a row of teeth, there are two facial CRJ lines—one wrapping around the outside of maxilla and one wrapping around the outside of the mandible. 
     A “lingual CRJ line” (also “rear CRJ line”) refers to an imaginary line extending across the face of a maxilla or mandible that passes through the rear and lowermost portion of the CRJ of each tooth or implant in the maxilla or mandible. Since the maxilla and mandible each have a row of teeth, there are two lingual CRJ lines—one extending along the inside of the maxilla and one extending along the inside of the mandible. 
     The “center” a two dimensional shape, such as cross-sections of the various implants described herein, shall mean the location on that two-dimensional body where the first moment of area equals zero. 
     The “mirror plane” that term is used herein is a plane that extends vertically through the implant from top to bottom, and extending front-to-back from the lingual side to the facial side of the implant. Each illustrated implant has a mirror plane. 
     The description below is of the dental implants that in whole or in part embody the invention described in the claims following this detailed description. In the discussion below, we explain several features and benefits of the dental implants—features and benefits that may or may not be incorporated in the device or methods described in the following claims. 
     The implants illustrated and described herein are all configured for use on the right side of the mandible and maxilla. The claims are intended to cover not only implants on the right side, but those on the left side as well. Non-illustrated implants for the left side of the mandible and maxilla are identical in construction to those on the right side, but are in mirror image form in the same manner as human teeth on one side of the mouth are mirror images of teeth on the opposite side of the mouth. 
     The features, capabilities and construction of each implant on the left side of the mouth (being of identical mirrored construction to those on the right side) are identical to the corresponding implant on the right side of the mouth. 
       FIGS. 1-7  illustrate a dental implant. The implant is a generally elongate member, with a lower portion or fixture  100  that is configured to be embedded or implanted in a maxilla or mandible, and an upper portion or abutment  102  that extends out of the maxilla or mandible and provides a structure on which a dental prosthesis  104  such as a crown, (colloquially called a “cap” and illustrated in  FIGS. 3-6 ), bridge or framework can be attached. 
     In the embodiment shown here, the crown  104  (which is illustrated as a dashed line) surrounds the upper portion of the implant, providing a smooth outer surface to simulate a natural tooth. The crown  104  extends above the marginal gingiva  106  (dashed) and for example slightly below the marginal gingiva. 
     Dental implants are generally provided either in one or in two pieces. By “one piece,” mean that the implant is a single integral body that is made to be implanted in a maxilla or mandible as a single unit, with an upper portion extending upward away from an out of the gingiva. 
     A two-piece implant, such as those shown in  FIGS. 25A  et. se. is made of two portions, the upper portion being generally referred to as the abutment and the lower portion being generally referred to as the fixture. In a two-piece implant, the abutment and fixture are coupled together, typically by a threaded fastener, and typically after the fixture has been implanted. 
     A “fixture” includes at least that portion of a dental implant that is inserted into a maxilla or mandible, or otherwise embedded in bone when in use. An “abutment” includes at least that portion of a dental implant that is configured to be coupled to and support a crown. Of course, there are combined fixtures and abutment arrangements in which the fixture and abutment are formed as a single unit. Examples include the one-piece implants illustrated in  FIGS. 1-24 . Thus, the terms “abutment” and “fixture” should not be interpreted as requiring a single piece dental implant. 
     The implant of  FIGS. 1-7  is a single piece implant, having an integrated abutment and fixture. It is intended for use as a lower central and lateral incisor. A similar single piece implant can be seen in  FIGS. 8-14 . It is intended for use as an upper lateral incisor. The description herein regarding the implant of  FIGS. 1-7  applies equally to the implant of  FIGS. 8-14  except where specifically noted as being applicable only to the implant of  FIGS. 1-7  or the implant of  FIGS. 8-14 . 
       FIG. 15  illustrates cross-sections of the fixtures or lower portions  100  of the implants  FIGS. 1-15  taken at cutting lines A-A, B-B, and C-C. These sections are sections through the lower portion  100  of the fixture. The cross-sectional shape  108  as shown in  FIG. 15  is circular. Each section in the lower portion of the fixture may have the same diameter or the same cross-sectional area. The lower section of the fixture and between cutting lines A-A, B-B, and C-C can have an irregular cross section, however, such as an oval or a polygon. The polygonal shape can be regular or irregular. The polygonal shape can have radiused corners. The polygon can be an convex or concavo-convex polygon.  FIG. 16  illustrates a regular convex polygon and cross-section  108 A having ten sides. The number of sides is not critical, however, although a range of between 6 and 15 would be beneficial. 
     There are advantages to using a fixture with a polygonal lower portion: when a fixture having a polygonal outer surface is inserted into a hole drilled into maxilla or mandible to receive the fixture, the gaps between the outer surface of the polygon and the circular drilled hole in which the fixture is inserted can be filled with a bone growth enhancer, autograft, allograft, or cement, for example. If the material is cement, it may help bond the fixture to the bone in which it is inserted. If the material is a bone growth enhancer, it may encourage bone growth between the fixture and the bone in which it is inserted, thereby providing more rapid healing and a better bond between the fixture and the bone in which it is inserted. Alternatively, the hole may be made by or profiled by an osteotome which may have an outer profile similar to the outer surface of the fixture. In this alternative method, a drill may be used to make the initial hole and the hole may then be expanded and profiled by inserting the osteotome straight down into the hole. 
     The implants of  FIGS. 1-14  have a longitudinal axis  110  that extends generally up-and-down through the length of the fixture (or lower portion  100 ) and through the abutment (or upper portion  102 ) as well. This axis is defined as a line as close to the center of mass of the lower portion of the fixture as possible. In at least some of the embodiments shown here, the cross-sections A-A, B-B and C-C are circular, and the longitudinal axis  110  goes through the center of the circular cross-sections. Were the cross-sections irregular, the longitudinal axis would pass through each cross section as close as possible to the real center of the cross sections as possible. 
     One can see from  FIGS. 15 and 16  that the longitudinal axis  110  goes through the center of each cross section. This indicates that in one embodiment, the lower portion  100  is not bent or curved, but is substantially straight (although the outer surface may taper in the shape of a flaring horn) along the length of the longitudinal axis such that the longitudinal axis extends through the center of all the cross-sections of the lower portion of the fixture  100 . 
       FIGS. 17 and 18  are cross sections of the upper portion of the fixture  100 . Note that the cross-sections may be not circular but extend irregularly, being narrower about one axis  112 , than about axis  114 . The cross-sections of  FIGS. 17 and 18  have the general cross-sectional shape of an ellipse. They also may be slightly flattened at one end of the major axis  112  to more accurately represent the profile of an incisor. Elliptical cross-section  116  ( FIG. 18 ), the upper cross section E-E of  FIG. 5  is larger in area and has a more distinct elliptical shape than elliptical cross-section  118 . 
     If one compares the lower circular cross-section  108  (i.e., A-A, B-B, and C-C) with elliptical cross-sections  118  and  116 , it is clear that the higher one moves up the fixture, the more elliptical and less circular the fixture becomes. Thus, the elliptical cross-section  118  shown in  FIG. 17  is more elliptical than the circular cross-section  108  shown in  FIG. 15  and the elliptical cross-section  116  shown in  FIG. 18  is more elliptical than the elliptical cross-section  118  shown in  FIG. 17 . 
     The more elliptical a cross-section of an ellipse is, the greater the major/minor axis length ratio of that ellipse as compared to another ellipse. For example, the major/minor axis length ratio of the ellipse  116  of  FIG. 18  is greater than the major/minor axis ratio of the ellipse  118  of  FIG. 17 , which in turn is greater than the major/minor axis ratio of the circle of  FIG. 15 . The ratio of  FIG. 15  is unity, since the cross-section shown in  FIG. 15  is a circle. 
     Note that the major/minor axis ratio of  FIG. 17  (1.05-1.25) is between that of  FIG. 15  (about 1.000) and  FIG. 18  (about 1.15-1.30). By providing a gradually increasing ellipticality (i.e. increasing major/minor axis ratio) as one progresses from the lower portion of the fixture to the upper portion of the fixture, the load provided by the abutment can be more equally distributed to the lower portion of the fixture and then to the mandible or maxilla. 
     One benefit to the increasing outward taper as one approaches the top of the fixture is that it more accurately represents the shape of a tooth at the equivalent height above the jawbone. Incisors, for example, have generally elliptical cross-sections at a height that corresponds to the height of section E-E ( FIG. 18 ). 
     By shaping the cross-section of the upper portion of the fixture as closely as possible to the cross-section of the real tooth that it replaces, the maxilla or mandible and the abutting mucosal tissue will better surround the implant in a contour that more closely resembles the bone contour of a natural, undamaged when the bone heals. 
     Furthermore, by helping the bone and tissue contour to regenerate closer to its natural shape, the gingiva which covers the bone will more closely imitate the original gingiva giving the patient a smile that is more regular, lifelike, and symmetric. 
     If the upper portion  101  of the fixture  100  is circular in cross-section, it is believed that bone will not heal along the natural bone contour. This could make the bone-to-implant junction weaker, and the gingiva more asymmetric and displeasing to the eye. By making the width of the upper portion of the fixture narrower in the interproximal direction, a gap is provided on either side of the fixture that gives the gingiva more room to grow between adjacent teeth or fixtures and to better surround the base of the tooth. 
     While the upper portion  101  of the fixtures  100  of  FIGS. 1-14  may have this irregular cross-sectional shape wider in the facial-lingual direction and narrower in the mesial-distal direction (see  FIGS. 17 and 18 ), it should be understood that an irregular shape is not essential. Indeed, any cross-sectional shape, such as the circular and regular polygonal shapes described above as possibilities for the lower portion of the fixture (see  FIGS. 15 and 16 ) are equally useful for the upper portion  101  of the fixture as well. 
     As we have shown, the lower portion of the fixture  100  may be circular and has a constant cross section as one moves up the fixture. The upper portion  101  of fixture  100  has a cross-section that may be non-circular and elongate in a fore-and-aft direction. The cross-sections of the upper portion  101  of the fixture  100  may be elliptical and may increase in cross-sectional area and irregularity (or out-of-roundness) as one moves up the upper portion of the fixture. 
     The cross-sectional area of each successive cross-section of the upper portion of the fixture may increase and make the fixture surface flare outward. This gives a greater and greater flare angle the farther one goes upward along the upper portion  101  of the fixture  100 . 
     By “flare angle” mean the angle between the longitudinal axis of the fixture and a line segment tangent to the surface of the fixture, wherein the line segment tangent lies in the same plane as the longitudinal axis of the fixture. The further up the upper portion of the fixture one goes, the greater the flare angle. As one moves up the fixture, the outer surface or wall of the fixture increases its angle with respect to the longitudinal axis or increasingly flares away from.  FIGS. 19A and 19B  illustrate this.  FIG. 19A  is a partial front and  FIG. 19B  is a partial side view of the implant of  FIGS. 1-7  showing the upper portion of the fixture. In  FIG. 19A , the flare angle of the outer surface or wall of the fixture is shown in three ( 3 ) locations  120 , 122 , and  124  along the longitudinal axis, where location  122  is above location  120  and location  124  is above location  122 . 
     The flare angle Ø at position  120  may be between 1 and 3 degrees. Traveling up the upper portion  101  of the fixture, the flare angle Ø at position  122  may be 2 and 5 degrees. Traveling even further up the upper portion of the fixture, the flare angle Ø at position  124  may be between 4 and 8 degrees. 
     Referring now to  FIG. 19B , the flare angle between the front wall of the upper portion of the fixture and the longitudinal axis is illustrated. 
     The flare angle Ø at location  120  may be between 3 and 8 degrees. The flare angle Ø at location  122  along the longitudinal axis may be between 6 and 12 degrees. The flare angle Ø at location  124  along the longitudinal axis of the fixture may be between 10 and 25 degrees. The flare angles of the back wall of the fixture are similar to those of the front wall at each location  120 ,  122 , and  124  flare angle at the front and back of the fixture is greater than the flare angles at each side of the fixture. 
     Another characteristic of the fixture is the increasing irregularity of its cross sections as one moves up along the upper portion of the fixture. For example, the cross-section shown in  FIG. 15  is regular: a circle. The cross-sections shown in  FIGS. 17 and 18  are less regular and more elliptical, with their area distributed farther from the center (or centric) of the area of the lower cross-sections A-A, B-B, C-C ( FIGS. 15 and 17 ). 
     Another characteristic of the fixture is the increasing normalized second moment of area of each of the fixture&#39;s successive cross-sections about the centroid of each said successive cross-section, as one progresses from cross-sections at the bottom of the upper portion of the fixture to and through successive cross-sections near or at the top of the upper portion of the fixture. 
     The second moment of an area (such as the cross-sections through the fixture) about a centric of that area is the sum over the entire area of each constituent infinitesimal area times the square of the distance of that infinitesimal area from the centroid of the overall area. In this case, the second moment of area is calculated about an axis that passes through the centroid of the cross-sectional area and is parallel with the longitudinal axis of the fixture. A normalized second moment of a (cross-sectional) area is the second moment of that (cross-sectional) area divided by the second moment of a circular disk having the same area as that (cross-sectional) area. 
     By this definition, the normalized second moment of the cross-sectional area of  FIG. 15  is one (1.0) since the actual cross-section of  FIG. 15  is a circular disk, and the longitudinal axis passes through the center. The normalized second moment of area of the circular cross-section  108  is the second moment of a circle having the area of cross-section  108  divided by the second moment of a circle of the same area. The illustrated cross-sections A-A, B-B, and C-C are already circles, the numerator and the denominator are the same, and therefore the ratio of second moments is one, regardless of the actual area of the circular cross-section of  FIG. 15 . By extension (1.0), the normalized second moments of area of the cross-sections of  FIGS. 17 and 18  are greater than one (1.0). Furthermore, the normalized second moment of area of the cross-section of  FIG. 18  is greater than that of the cross-section of  FIG. 17 . 
     By increasing the second moment of area in successive cross-sections of the upper portion of the fixture, loads placed on the abutment can be more effectively distributed and transferred to the bone that surrounds the lower portion of the fixture. 
     The normalized second moment of area may increase as one moves upward through successive cross-sections of the upper portion of the fixture, as explained immediately above. This increase in normalized second moment may be continuous and unbroken as one moves upward through the fixture. By “continuous and unbroken” it is meant that successive cross-sectional areas of the upper fixture&#39;s cross-sections meet the requirement that their normalized second moment (as described above) is greater than the normalized second moment of the cross-section immediately below, and is smaller than that of the cross-section immediately above. 
     Another characteristic of a possible embodiment of the fixture is that the flare angle of its walls changes at different rates depending upon circumferential position around the longitudinal axis where that flare angle is measured. 
       FIGS. 19A and 19B  show how the outer surface of the fixture flares at four different locations around its periphery at three successively higher longitudinal positions  120 ,  122 , and  124 . Note that the flare angle increases at different rates depending upon the location around the periphery or circumference of the fixture. The term “rate of flare” used here means the rate at which the flare angle increases per unit of distance traveled upward along the longitudinal axis of the fixture. In  FIG. 19A , the flare angle of the side walls of the upper portion of the fixture, change from Ø 1  equals 2 degrees at location  120  to Ø 2  equals 3.5 degrees at location  122 . This gives a rate of increase of the side wall flare angle of 1.5 degrees over the distance traveled from location  120  to location  122 . In  FIG. 19B , at location  120 , the flare angle is Ø 4  equals 4.5 degrees and at location  122 , the flare angle is Ø 5  equals 9 degrees. The rate of change of the flare angle as one travels from location  120  to location  122  along the longitudinal axis of the fixture is 9 degrees minus 5.5 degrees or 3.5 degrees. This is greater than the 1.5 degrees increase in flare angle measured along the side wall of the fixture as shown in  FIG. 19A . Locations  120 ,  122  and  124  are spaced equally far apart. Thus, depending on one&#39;s position around the periphery of the upper portion of the fixture at a particular position along the longitudinal axis, the flare angle varies and the rate of change of the flare angle (the rate of flare) varies as well. 
       FIGS. 2 and 9  are top views of the fixtures of  FIGS. 1-14  showing how the tops of the fixtures may extend radially outward away from the base of the abutment, may face upward and define a narrow band  126  that extends outward away from the lower portion of the abutment and generally perpendicular to axis  110 . This narrow band  126  may be not circular in plane view, but instead has an irregular outer profile such as the elliptical profile shown in the cross-sections D-D and E-E of  FIGS. 1-14 . The width (“W” in  FIG. 20 ) of the narrow bands  126  (i.e. their extent in the radial direction—the directions perpendicular to axis  110 ) may be constant as one travels around the periphery of the fixture and may measure between 0.25 mm and 1 mm. 
     The top of the fixtures intended for different tooth positions along the mandible may have different contours, each contour mimicking the contours of the tooth that is being replaced since the shape of the upper portion of the fixture in the mouth may have different contours. The contours of this narrow band may vary from implant to implant depending upon the location along the mandibles. 
     As one follows the band around the circumference of the fixture the path described by band may rise and fall—it may move up and down along the longitudinal axis of the implant as shown in the embodiments herein. By “rising” it is meant that it moves upward. By “falling”, it is meant that it moves downward. 
     Referring now to the front views of the incisor implant shown in  FIGS. 21-23  note how in each case the band falls to a lowest point or minima  130  at the rear of the implant at a position  132  along the implant&#39;s longitudinal axis. 
     In the left side view of the implants, shown in  FIG. 22 , note how the band rises to a local high point or maxima  134  at a position  136  along the longitudinal axis of the implant. There is a similar maxima  135  on the opposite side of the implant at the same position  136 . 
     In the front view of the incisor implant shown in  FIG. 23 , note that the band again falls to a second local low point or minima  138  at position  140  along the longitudinal axis at the rear of the implants. 
     Thus, each implant has two local minima located at the front and the back of the implant, and two local maxima located at both sides of the implants. Looking at the implants in a direction perpendicular to the implant&#39;s longitudinal axes, such as the views shown in  FIGS. 21-23 , one can see a relative relationship of the local minima with respect to the longitudinal axis. Note that the highest points on the band are the two local maxima  134  and  135  located on either side of the band. The front local minima  138  is below the two local maxima  134  and  135  and the rear local minima  130  is below the front local minima  138 . 
     By locating the minima and maxima as shown, the thrust loads of the tooth are more evenly resisted when the crown (see  FIGS. 3-6 ) presses down against the surface of the narrow band. 
     This rise and fall of the band from maxima to minima to maxima to minima and back to maxima as it extends around the circumference of the implant varies depending upon the intended installed location of the implant, since the loads are different in each location. 
     The narrow band  126  may define a planar surface or a plurality of intersecting planar surfaces. As best shown in the side view of  FIG. 22 , the band  126  defines two imaginary planes  142  and  144  that intersect at the upper maxima  134  and  135 . 
     Since the intersecting planes  142  and  144  intersect, they are, by definition, at an angle to one another. They also may be at an angle to the longitudinal axis  110 . As shown in  FIG. 22 , the plane  144  defining the front half of the narrow band  126  may be at an angle alpha of between 5 and 15 degrees with respect to the longitudinal axis. It may also be at an angle of between 7 and 30 degrees. 
     The above angles are the angles between the plane and the longitudinal axis as it would appear when projected into a view normal to the longitudinal axis, which in this embodiment is the side view. 
     The other intersecting plane  142  defines the rear half of the narrow band  126  of the incisor implants of  FIGS. 1-15 . It, too, may be at an angle with respect to the longitudinal axis. The angle beta may be between 10 and 50 degrees. It may be between 15 and 40 degrees. It may be between 20 and 55 degrees. 
     The above angles are the angles between the rear plane and the longitudinal axis as it would appear when projected into a view normal to the longitudinal axis, which in this embodiment are the side views. 
     The abutment or upper portion  102  of the implants of  FIGS. 1-14  may taper inwardly (i.e. toward axis  110 ) from the base as the abutment extends upward away from the fixture. Successive cross-sections of the abutment (by a plane perpendicular to axis  110 ) get smaller and smaller in area as one moves upward along the longitudinal axis  110  from the base  150  of the abutment  102  to the top  152  of the abutment. See, for example,  FIGS. 21-23 . The base  150  of the abutment adjacent to the fixture may be one continuous curved surface  154  extending circumferentially around the implant. Surface  154  is tapered inwardly toward the longitudinal axis as it moves upward, having a smaller and smaller cross-sectional area. 
     The base  150  of the abutment where the abutment meets the fixture  100  may be disposed radially inward around the entire circumference of the implant. It is this inward spacing of the abutment away from the edge of the top of the fixture that defines the narrow band  126  described in greater detail above. 
     The base  150  of the abutment may have a cross-sectional shape similar to that of the fixture to which it is coupled. For example, the implants of  FIGS. 1-14  have fixtures with upper surfaces and cross-sections that are generally flattened ellipses and hence have major and minor axes. The abutments that extend upward from these fixtures have cross-sections similar to the top portions of the fixture to which they are coupled. They also may be flattened ellipses. 
     Another similarity is that the base of the abutment and the top portion of the fixture have the same number of “nodes”. A “node”, as the term is used here, describes local protrusions of curvilinear shapes (e.g. regions wherein the circumferential periphery of the implant has a reduced radius of curvature or regions where the periphery curves more sharply). A node exists on each flattened ellipse wherever there is a local minima in the radius of curvature. The three nodes (the three local minima) on the flattened ellipse  159  defined by base of the abutment are identified as items  160 ,  162  and  164 . The three nodes on the flattened ellipse  161  defined by the top of the fixture and corresponding in circumferential location to nodes  160 ,  162  and  164  are  166 ,  168  and  170 . There are as many nodes as there are minimas of the radius of curvature function as one travels around the periphery of the ellipse. These nodes protrude from their respective flattened ellipses, two at the flattened end  172  of the ellipse at one end  174  of the major axis  176 , and one at the other end  178  of the ellipse at the other end of the major axis  176 . 
     Note that the nodes  160 ,  162  and  164  of the abutment are aligned with corresponding nodes  166 ,  168  and  170  of the fixture as best seen in  FIG. 24 . The nodes of each fixture and its corresponding abutment are distributed at the same angular locations around the longitudinal axis of the implant. For the fixture of  FIG. 24 , node  168  is disposed at 40 degrees, node  170  is disposed at 180 degrees and node  166  is disposed at 320 degrees. For the abutment of  FIG. 24 , node  162  is disposed at 35 degrees,  164  is disposed at 180 degrees and node  160  is disposed at 325 degrees. These angles are measured with respect to a plane extending fore-and-aft and passing through longitudinal axis  110  of the implant. 
       FIGS. 3-6  illustrate an exemplary orientation of an implant and its associated prosthesis, shown as crown  104 . The implant shown in  FIGS. 3-6  shows a coupling of an implant and a crown. Note that the crown  104  extends around and completely covers the free portion of the abutment—e.g. the free outer surface of the abutment extending above the top of the fixture. The lower portion of the crown abuts the fixture, more particularly, the surface of narrow band  126 . 
     The junction created by the lower portion of the crown  104  abutting the narrow band is smooth. The junction is configured to provide a smooth transition from the crown to the fixture, and vice versa. 
     In the embodiments of  FIGS. 1-24 , the fixture and the abutment are unitary structures, formed integrally, or formed individually and coupled together to one another before implantation in the maxilla or mandible. For most applications, however, it is desirable to create a multi-piece device having an abutment and fixture that are separate and removably attachable. 
     In a system using a separately installable fixture a doctor is enabled to implant a fixture, to wait for the fixtures and bone to heal, and to then attach an abutment and crown to the fixture. This delayed assembly permits a fixture to heal before a tooth load is applied. If the entire implant, both fixture and abutment, was installed initially, the patient could only with great difficulty avoid biting down on the implant while the bone heals. Biting forces applied to an implant, especially during the initial fixtures/bone healing phase, can prevent proper healing. 
     The implants of the following figures ( FIGS. 25A  et seq.) are all two-piece implants in which the abutment and the fixture are separate and are coupled together after the fixture is embedded in a patient&#39;s bone and permitted to heal. In each of the examples of  FIGS. 25A  et. seq. the abutment and fixture are held together with a screw, and have interengaging binding surfaces that prevent rotation of the abutment with respect to the fixture. 
       FIGS. 25A-26D  show structures that couple the abutment and the fixture. 
       FIGS. 26A-26C  show the fixture portion of a two-piece implant in top, side, and rear views, respectively. Exemplary fixture  180  has a hole  182  that extends axially down the middle of the fixture to a depth of between 3 and 10 mm. This hole is a right circular cylinder and has internal threads  184  that are configured to engage a screw ( FIG. 26D ) that extends through the abutment ( FIGS. 25A-25D ) into the fixture. 
     An upper portion  186  of the hole is a right circular cylinder and has a larger diameter than the lower threaded portion  188  of the hole. This upper portion also has an antirotation structure  190 , here shown as a half-circle slot that is formed in the wall of the upper portion of the hole  182 . This slot defines a surface that interengages with the abutment to prevent the abutment and the fixture from rotating with respect to each other. 
     Slot  190  may be shaped as an arc of circle as viewed from above and as best shown in  FIG. 26A . The transition between the slot  190  and the upper portion  186  may be rounded or radiused. 
     The diameter of the upper portion  186  of hole  182  may be between 1.2 and 1.7 larger than the diameter of the lower threaded portion  188  of hole  182 . 
     The upper portion  186  of the hole may have a constant diameter, or it may be tapered inward the farther one goes down upper portion  186  to have a smaller and smaller cross-sectional area. If tapered, the taper angle (the angle between the longitudinal axis of the hole and the wall of the upper portion) may be between 1 and 10 degrees. 
     Note that the upper surface  192  of the fixture is generally planar, in the form of two intersecting planes  194  and  196 . These planes join together at a line  198  that extends across the top of the fixture from one side to another, dividing the top of the fixture into two portions of generally equal area. By generally equal, we mean that the area of the top surface of the fixture on one side of line  198  is between 0.8 and 1.25 times the size of the area on the other side of the line. 
     In  FIGS. 25A-25D , the abutment  200  has a central hole  202  that extends entirely through the abutment. This hole is slightly larger in diameter than the threads of the screw ( FIG. 26D ) designed to mate with threaded hole  188  in the fixture. 
     The upper portion  204  of central hole  202  has a larger diameter than the lower portion  206  of central hole  202 . The bottom  208  of the upper portion  204  defines a planar surface  210  that is configured to receive and support the head  203  of the screw  205  ( FIG. 26D ) that holds the abutment and fixture together. 
     A cylinder  214  extends downward from the bottom surface  216  of the abutment. This cylinder is configured to fit inside the upper portion  186  of the hole  182  in the fixture. The cylinder  214  may be a right circular cylinder, although it may have a taper matching that of the upper portion of the hole in the fixture. Cylinder  214  includes an arcuate projection  215  generally the same in size and orientation as the arcuate slot  190  in the fixture. 
       FIG. 26D  is a partial cross-section of the abutment and fixture of  FIGS. 25A-25D  and  26 A- 26 C, showing how they are fixed together by screw  205 . 
     Cylinder  214  is inserted into upper portion  186  of hole  182 . The head  203  of screw  205  is configured to enter the upper portion  204  of abutment hole  202  and may be received entirely therein such that it does not extend above upper surface  212  of abutment  200 . 
     The lower surface  216  of the abutment  203  from which the cylinder  214  downwardly extends is in the form of two intersecting planes  218  and  220 . These planes may be at the same angles with respect to one another and with respect to axis  110  as are planes  194 ,  196 , respectively that form the top of the fixture such that when the fixture and abutment are coupled together, plane  218  abuts and is generally coplanar with plane  194  and plane  220  abuts and is generally coplanar with plane  196 . Plane  218  and plane  194  may be parallel, as are planes  220  and  196 . Furthermore, the angle between planes  194  and  196  on the fixture is the same as the angle between planes  218  and  220  on the abutment. 
     The planes  194  and  196  that define the top of the fixture have a greater overall area than the overall area of planes  218  and  220  that define the bottom of the abutment. When the cylinder extending from the abutment is inserted into the upper portion of the hole in the fixture, the planes  194  and  196  defining the top of the fixture extend radially outward beyond the planes  218  and  220  that define the bottom of the abutment. This portion of planes  194  and  196  extending beyond the bottom of the abutment define a narrow band  126  that extends around the implant. 
     This narrow band  126  that extends outward from the junction of the abutment and the fixture that is formed by the planar top surface of the fixture may have the same characteristics, extent and orientation as the narrow band  126  described as part of the single piece implant of  FIGS. 1-24 . 
     There are several alternative fixture and abutment couplings that are also considered beneficial. 
     For example, rather than having one arcuate projection  215  on the abutment&#39;s cylinder that mates with one arcuate slot  190  in the fixture&#39;s hole, more may be provided, such as two, three, four, five, six, seven, or even more. 
     The slot/projection pairs that engage with each other to prevent rotation of the abutment with respect to the fixture may be arranged equiangularly about the longitudinal axis of the implant. For example, if there are two such slot/projection pairs, they may be disposed at 180 degrees with respect to each other about the longitudinal axis. If there are three, they may be located at 120 degrees with respect to each other. If there are four pairs, they may be disposed at 90 degrees, and so on. 
     In another alternative embodiment, rather than having a cylinder projecting downward from the abutment that, in turn, mates with a similarly shaped hole in the fixture, their positions may be reversed: the cylinder may extend upward from the fixture to be received in and engage a hole extending upward into the bottom of the abutment. In this case, the sizes, shapes and orientations of the cylinder and its receiving hole in  FIGS. 25A-26D  are the same, merely reversed. 
     In yet another alternative embodiment, rather than arcuate slots and projections, the slots and projections may be polygonal, for example triangular ( FIG. 27 ), trapezoidal ( FIG. 28 ), or rectangular ( FIG. 29 ). 
     Instead of the circular cylinder and hole arrangement shown in  FIGS. 25-26 , the cylinder (and the hole that receives) it may be faceted, defining mating surfaces with longitudinally extending interengaging facets that provide the anti-rotation feature of the mating slots and projections ( FIG. 30 ). If faceted, the facets on the cylinder and in the hole in which it is inserted may define a regular polygon when viewed along the longitudinal axis of the implant. 
     The circular cylindrical hole and mating cylinder can be circular, ovoid, elliptical, or have any other smooth curvilinear irregular surface that assists in preventing rotation of the abutment with respect to the fixture. 
     The cylinder, whether extending downward from the abutment, or alternatively extending upward from the fixture, may have protruding surfaces that engage slots or grooves on the hole. The protrusions or projections  215  may be provided on the inner surface of the hole, extending inwardly, and the slots or grooves to which they are mated may be provide on the outer surface of the cylinder. See  FIG. 31 , for example. In short, the slots  190  and projections  215  may be reversed. Any of the above arrangements and configurations of the mating surfaces of the abutment and the fixture can be combined to provide additional anti-rotation capability. For example, the shapes may have corners such as those illustrated in these figures but may also have rounded engaging surfaces such as those shown in the fixtures of  FIGS. 115  et seq., or any combination of corners and curvilinear surfaces. 
       FIGS. 32-59  illustrate two-piece implants that may be used as replacement for cuspids.  FIGS. 32-45  illustrate a replacement implant for an upper (i.e. maxillary) cuspid.  FIGS. 46-59  illustrate an implant for a lower (i.e. mandibular) cuspid. 
     The cuspid implants shown herein are two piece implants (not including fasteners), as illustrated herein, and have coupling structures such as those shown in  FIGS. 25-31 , described above. While they are illustrated as two-piece implants, they may also be provided in single piece form. In single piece form, they would have the identical structural characteristics, capabilities and features as the two piece upper central incisor implant shown in  FIGS. 25-31 , but would lack the coupling feature (i.e., the holes, cylinders and screws) of  FIGS. 25-31 . 
     All the two piece implants ( FIGS. 25A  et seq.), when assembled, have the same configuration, structures, benefits, shapes, sizes, orientations, and uses as the single piece implants of  FIGS. 1-24 . The illustrated embodiments differ in the differential characteristics identified in the discussions accompanying each of the  FIGS. 32  et. seq. below. Furthermore, each of the two piece fixtures of  FIGS. 32  et seq. may have the same illustrated and alternative coupling structures as described above in conjunction with  FIGS. 25A-31 . 
     The angle  300  of the planar top  302  of abutment  102  through which hole  202  passes is 135 to 165 degrees with respect to the longitudinal axis  110  of the implant for the upper cuspid and 180 to 150 degrees with respect to the longitudinal axis  510  of the implant for the lower cuspid. 
       FIGS. 60-73  illustrate a two-piece implant that may be used as replacement for first lower premolars.  FIGS. 60-66  illustrate the abutment portion  102  and  FIGS. 67-73  illustrate the fixture portion  100 . Abutment  102  has an upper surface  302  that unlike the prior examples is not a flat plane, but is a compound concave convex surface as shown in the side view of  FIG. 64 . A lower portion of surface  302  is disposed at an angle  300  with respect to longitudinal axis  110  of 120 degrees. An upper portion of surface  302  is disposed at an angle  300  prime with respect to longitudinal axis  110  of 160 degrees. An upper portion  304  of surface  302  is concave. A lower portion  306  of surface  302  is convex. 
       FIGS. 74-87  illustrate a two-piece implant that may be used as a replacement for first upper premolars.  FIGS. 74-80  illustrate the abutment  102  portion of the implant and  FIGS. 81-87  illustrate the fixture  100  portion of the implant. 
     Abutment  102  has an upper surface  310  that defines 2 local maxima  312  and  314  and 2 local minima  316  and  318 . These are arranged such that the 2 maxima  312  and  314  are generally aligned with and extend along the fore-and-aft axis  320  and the 2 minima  316  and  318  are disposed along the orthogonal side to side axis  322 . In this context, fore-and-aft refers to an axis extending from the lingual side to the labial side of the implant and side to side refers to an axis extending perpendicular to that direction along the mandible or maxilla toward adjacent teeth. 
     In plan view, upper surface  300  of abutment  102  is convex. The lower portion  159  of abutment  102  as seen in plan view ( FIG. 75 ) is convex-concave. It generally has a kidney shape with one side wall  324  that is concave. The lower portion  159  of abutment  102  has four nodes  326 ,  328 ,  330 , and  332  generally disposed at the four corners of the abutment with two nodes  330  and  332  facing outward on the labial side and two nodes  326  and  328  facing inwards on the lingual side of the abutment. Side wall  324  changes from concave at a lower portion  334  of the side wall to convex at an upper portion  336  of the side wall. 
     Abutment  100  similarly has an upper surface  161  that is concavo-convex in plan view ( FIG. 82 ). Surface  161  has four nodes  338 ,  340 ,  342 , and  344  that are disposed about longitudinal axis  110  in the same angular orientation as corresponding nodes  330 ,  328 ,  326 , and  332 , respectively. In a similar fashion, an upward wall portion  346  is concave and is angularly disposed with respect to longitudinal axis  110  in the same location as concave portion  334  of surface  324  of abutment  102  shown in  FIG. 74-80 . Nodes  338  and  334  face outwardly on a labial wall of the fixture  100  and nodes  340  and  342  face inwardly (lingually) on the opposing side of abutment  100 . Top surface  161  of abutment  100  has a kidney shape oriented in the same manner as the kidney shape lower portion  159  of abutment  102 . 
     The fixture concavity and the abutment concavity may be disposed one above the other at the same angular location and on the same side of the implant. In the example shown here, the concavity is on the right side of the implant. The right side of the implant is also the side of the implant closes to the front of the mouth. It is the side of the implant that, when inserted, will face and abut either the first upper cuspid or a first upper cuspid implant. 
     The shape of the concavity may be sized to receive a portion of the convex side of the adjacent cuspid. In this manner, the concavity permits the cuspid and the first premolar to be fitted together more closely, with a convex sidewall of the cuspid tooth or implant nested inside the concavity of the first upper premolar. 
     The concavity of the abutment is similarly reduced as one moves in the opposite direction by rising upward from the concave region toward the top of the abutment. Just as with the fixture, this transition from concavity to convexity is gradual, with the radius of curvature gradually increasing until the wall of the abutment flattens. Above the height that it flattens, the sidewall of the abutment becomes convex. At the same time, the cross-sectional shape becomes rounder, and the four nodes are reduced to three nodes at the top of the abutment, as best shown in the top view of the abutment, FIG.  75 . 
       FIG. 82  includes a dashed line  350  that shows the position of lower portion  159  of abutment  102 . The space between line  350 , the outer most extent of the lower portion of the abutment and upper edge  352  of fixture  100  defines the narrow band  126  in this example. Note that narrow band  126  when projected in the top view ( FIG. 82 ) is concavo-convex and includes an indented or concaved portion  354  unlike the preceding examples. 
       FIGS. 88-101  illustrate a two-piece implant that may be used as a replacement for lower molars (LM).  FIGS. 88-93  illustrate the abutment  102  portion, and  FIGS. 94-101  illustrate the fixture  100  portion. 
     The LM implants have four nodes  360 ,  362 ,  364 , and  366  at the top of the fixture  161 , four corresponding nodes  368 ,  370 ,  372 , and  374  at the bottom  159  of the abutment  102 . These nodes on the abutment are angularly aligned with the nodes on the fixture at the bottom of the abutment, and at the top of the abutment. These four nodes are disposed at four angular locations measured in a circumferential direction with respect to the longitudinal axis  110  of the LM implant. 
     The rounded corners of the abutment  102  that define the nodes typically extend upward and tilt slightly inward, as shown in the FIGURES, to make a four-sided generally pyramidal structure. 
     The abutment may be a polygonal (for example a quadrilateral or trapezoidal) pyramidal cylinder with rounded corners, as shown herein. Each face of the pyramidal shape  383 ,  382 ,  384 , and  386  is a sidewall of the abutment. Each sidewall may meet at a corner. These corners where adjacent sidewalls of the abutment meet are rounded. Each corner is one of the four nodes of the abutment. 
     One sidewall of the abutment, the lingual sidewall  386  faces inward toward the tongue. One sidewall, the facial sidewall  382  faces outward toward the face. The lingual sidewall may be shorter than the facial sidewall. The sidewalls  380  and  384  that join the lingual and facial sidewalls therefore spread apart as they extend forward from the lingual sidewall to the facial sidewall. 
     The top surface  300 , while generally planar and parallel to the longitudinal axis of the implant, has four prominences or peaks  390 ,  392 ,  394 , and  396  that extend upward from the top surface  300  of the abutment  102 . These prominences or peaks (local maxima) are disposed one at each rounded corner of the abutment. 
     The width of the LM implant&#39;s narrow band  126  may be between 0.5 and 1 mm. 
     Inner or lingual side wall  386  of abutment  102  may be slightly concave, both at the top and at the bottom where it abuts the top of fixture  100 . Upper portion  400  of the side wall of fixture  100  may be concave to the same extent as the concavity of abutment  102  thereby defining there between a slightly concave portion  402  of narrow band  126 . This concave portion  402  of narrow band  126  is located on the lingual side of the implant fixture  100 . 
       FIGS. 102-115  illustrate a two-piece implant that may be used as a replacement for upper molars (UM).  FIGS. 102-108  illustrate the abutment  102  portion of the UM implant and  FIGS. 109-115  illustrate the fixture  100  portion of the UM implant. 
     The UM implant have three nodes  410 ,  412 , and  414  located at the bottom  159  of abutment  102 . There are three corresponding nodes  416 ,  418 , and  420  that are angularly disposed about longitudinal axis  110  in the same location as corresponding nodes  410 ,  412 , and  414 . UM abutment  102  has four peaks or prominences (or maxima) that extend upward from top surface  300  of that abutment. Each of these four prominences  430 ,  432 ,  434 , and  436  are spaced apart from adjacent peaks or prominences by an angle of between 70 and 120 degrees about longitudinal axis  110 . 
       FIGS. 116-123  are top, bottom, left, rear, right, front, perspective, and cross-sectional views, respectively, of abutment  600 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 124-130  are front, cross-sectional, rear, left, top, bottom and perspective views of fixture  502 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 163 ,  164  illustrate the assembled alternative implant  501  comprised of the abutment  600  of  FIGS. 116-123 , the fixture  502  of  FIGS. 124-130 , and a threaded fastener  700 . In  FIG. 163 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and front-to-rear. In  FIG. 164 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and side-to-side. 
     An identical (but mirror image) implant to the one of  FIGS. 116-130 ,  163 ,  164  can be used to replace lateral incisor #10. This implant is identical in all respects to implant  501  but in mirror image form and therefore has not been separately illustrated and described herein. 
     Referring now to  FIGS. 124-130 , a dental fixture, here shown as lateral incisor fixture  502  is illustrated. Fixture  502  includes a lower portion  504  that is formed integral with an upper portion  506 . Fixture  502  includes a longitudinal axis  508  that extends from the lower hemispherical tip  510  of the lower portion  504  to the top of fixture  502 . 
     Lower portion  504  is generally circular in longitudinal cross-section having a smaller diameter at a lower end of portion  504  and a larger diameter at the upper end of portion  504 . Portion  504  is generally conical with an included flare angle of 12 degrees. This angle may be symmetric about the longitudinal axis  508  of the lower portion  504 , such that the cone defined by the major diameter of the threads extends outward from the longitudinal axis  508  by 6 degrees. 
     This taper permits the threads to be progressively wedged into the maxilla with each successive turn of fixture  502  about its longitudinal axis. As fixture  502  is rotated, it extends deeper into the bone and extends farther outward in a direction normal to the longitudinal axis  508  of fixture  502 , causing each turn of thread  514  to wedge more firmly into the bone. In an alternative arrangement, the fixture can be press fit into the prepared hole (also called an “osteotomy”). 
     Lower fixture portion  504  is threaded over substantially all of its length. Thread  514  extends from the upper part of hemispherical tip  510  to the upper end of the threads located generally at the longitudinal midpoint  516  of fixture  502 . 
     Thread  514  has an asymmetric profile, best shown in  FIG. 124 . Thread  514  is a single helical thread that extends the length of lower portion  504  of fixture  502  and has a pitch of 0.576 mm, a depth of 0.5 mm, and a length in an axial direction of 6.0 mm. It flares outward at an angle A of 6 degrees from the longitudinal axis ( FIG. 127 ) as it extends upward. 
     Thread  514  is broken by two longitudinal semi-circular grooves  518 ,  520  that are provided on the outer surface of fixture portion  504 . The grooves are disposed at an angle B of 180 degrees from one another ( FIG. 129 ) as measured in a plane normal to the longitudinal axis  508 . Groove  518  extends vertically along the outer front surface of fixture portion  504 . Groove  520  extends vertically along the outer rear surface of fixture portion  504 . The thread is broken by these grooves (i.e. it does not extend across the grooves). When the fixture is screwed into the bone of the patient&#39;s mouth, grooves  518 ,  520  provide a longitudinally extending void into which bone may grow. Bone that is encouraged to grow into grooves  518 ,  520  prevents the rotation of the fixture when the fixture is twisted about its longitudinal axis. These grooves also allow for fluid evacuation when press fit into the osteotomy. They also ensure the threads do not come through the facial bone of the maxilla. 
     The upper portion  506  of fixture  502  is substantially the same length (measured in a longitudinal direction) as lower portion  504 . The outer surface profile of upper portion  506  differs from portion  504 , however. The outer surface  526  of the lower end of upper portion  506  is circular in cross-section with an outer diameter approximately the same as the root diameter of threads  514 . As upper portion  506  extends upward toward its upper end, however, this cross-sectional profile changes from a circular profile to a generally oblate and elliptical profile. The outer surface  528  of the upper end of upper portion  506  is generally elliptical in cross-section. 
     The outer surface  528  has a major axis  530  and a minor axis  532  ( FIG. 128 ), with the major axis  530  extending generally front-to-rear in a facial-to-lingual direction when installed in the patient&#39;s mouth, and minor axis  532  extending generally left-to-right in a mesial-distal direction when installed in the patient&#39;s mouth. 
     When viewed in front view and rear view ( FIGS. 124 ,  126 , respectively), the left and right side walls of upper portion  506  adjacent to thread  514  flare outward in the mesial and distal directions at an angle C of about 9-11 degrees with respect to the longitudinal axis  508  as they extend upward. About halfway up upper portion  506 , the sidewalls flare outward at a slightly smaller angle D of about 3-7 degrees with respect to longitudinal axis  508 . 
     When viewed in side view ( FIGS. 125 ,  127 ), the side walls of the upper portion  506  at the left and right ends of the major axis flare outward in the lingual and buccal directions at an angle E of about 20-22 degrees from the longitudinal axis  508  as they extend upward. About halfway up upper portion  506 , the sidewalls flare inward at a smaller angle F of 1-7 degrees with respect to the longitudinal axis  508 . 
     The top surface of the fixture is in the form of two intersecting planar surfaces, a front surface  536 , and a rear surface  538  that are pierced by an irregularly shaped hole  540  extending downward in the axial direction into upper portion  506  of fixture  502 . Surfaces  536 ,  538  intersect to define two local maxima (or peaks)  542 ,  544  of the fixture on the left and right side of the fixture, respectively. These two maxima define the uppermost extent of the fixture on each side. 
     The two surfaces  536 ,  538  of top surface of fixture  502  are radiused or curved where they intersect and do not meet at a sharp line (for example as illustrated in the embodiment of  FIG. 20  in which the front and rear surfaces of the top of the fixture intersect along a line that defines maxima  134 ,  135 ). In the embodiment of  FIGS. 116-124 , this radiused intersection provides two curved crests or peaks (i.e. maxima  542 ,  544 ) located on opposite sides of the top of the fixture. Surfaces  536 ,  538  are not curved to the same degree where they meet. Instead, they are curved more steeply on the left side of the fixture  502  such that the local maximum  542  is not as high as the local maximum  544  on the other side of the fixture  502 . 
     Similarly, the two surfaces  536 ,  538  intersect hole  540  at two local minima  541 ,  543  located at the front and back, respectively, of fixture  502 . The rim of hole  540 , where it intersects top surfaces  536 ,  538  defines a continuously curved path around the upper edge of hole  540  between local maxima  542 ,  544  disposed on the left and right sides, respectively, of the fixture  502  and local minima  541 ,  543  located at the front and back, respectively, of fixture  502 . 
     Hole  540  is irregularly shaped, having a cross-sectional profile at its upper end that is substantially elliptical with a major axis extending front to rear and the minor axis extending left to right. As one descends into hole  540 , the hole transitions from a substantially elliptical shape to a substantially circular shape having a diameter that may be less than half the length of the minor axis at the top of the fixture. As one descends into hole  540 , the major axis is reduced in length at a rate greater than the minor axis is reduced in length. In other words, the circular bottom of hole  540  flares outward in a front to rear direction at a rate greater than it flares outward in a side to side direction as one ascends from the bottom of hole  540  to the top of hole  540 . It is this differential rate of flaring that transitions the hole from a circular cross-section at its base to a generally elliptical cross-section at its upper end. 
     The configuration of hole  540  has several advantages. First, by tapering the hole in this manner, a dental abutment (discussed later herein) can be coupled more firmly to fixture  502  by the wedging effects and the frictional engagement of the external surface  608  of the lower portion of the abutment  600  to the inner wall of hole  540 . Furthermore, by providing hole  540  into an irregular, noncircular longitudinal cross-section over substantially all of its length, the rotation of the abutment with respect to the fixture can be eliminated. Even further, by providing hole  540  with a profile in cross section that has a continuous curve over substantially all of its length (in this case a generally elliptical surface) the sharp corners or other protrusions that serve as anti-rotation structures of  FIGS. 27-31  herein, can be eliminated, and a closer mating between the sidewall of hole  540  and the outer wall of the abutment (discussed below) can be provided as well as a reduction in stress risers by the reduction in sharp transitions (e.g. corners) and the provision of a larger surface area to reduce localized stress. By more closely mating the abutment to hole  540  in the fixture, voids or gaps between the abutment and the fixture can be reduced or eliminated, thus reducing or eliminating the ability for biological matter to accumulate in these voids or gaps and provide a reservoir for infection. 
     Hole  540  has a generally flat bottom ( FIG. 125 ) into which a second threaded hole  548  extends. Hole  548  is smaller in diameter than the bottom of hole  540  and serves to anchor the abutment inserted into hole  540  in place. 
     The sidewall of hole  540  is formed as a smooth continuously curved surface having no sharp transitions such as edges or corners between intersecting planes that could create voids and gaps that accumulate biological matter and provide a reservoir for infection. The cross section of hole  540  is elliptical in cross section at its upper end, and tapers smoothly to a circular cross section at its lower end. The elliptical major axis  550  ( FIGS. 125 ,  128 ) of hole  540  at its upper end is oriented generally front-to-rear (i.e. facial-to-lingual) and its minor axis  552  ( FIGS. 124 ,  128 ) is oriented generally side-to-side (mesial-to-distal). The major and minor axes ( 530 ,  532 ) of the outer surface of the upper portion  506  and the major and minor axes ( 550 ,  552 ) of the hole  540  are generally aligned, but rotationally displaced from each other by an angle G ( FIG. 128 ) of about 35 degrees about the longitudinal axis  508 . 
       FIGS. 116-123  illustrate a dental abutment  600  that is configured to engage the dental fixture illustrated in  FIGS. 124-130 . Dental abutment  600  is an elongate structure having a longitudinal axis  602 . It is formed as a unitary monolithic elongated body that has an upper portion  604  and a lower portion  606 . 
     Lower portion  606  is generally cylindrical and has a smooth continuous external surface  608  that is revolved around the longitudinal axis  602  and tapers outwardly over its entire length from the bottom of lower portion  606  to the top of lower portion  606 . The lower end of lower portion  606  is circular in axial cross-section. The upper end of lower portion  606  is generally elliptical in axial cross-section. The major axis  610  ( FIG. 117 ) of the elliptical cross-section of abutment  600  extends front-to-rear (e.g. facial-to-lingual). The minor axis  612  of the elliptical cross-section of abutment  600  ( FIG. 117 ) extends side-to-side (e.g. mesial-to-distal). 
     In order to achieve this circular cross-section to elliptical cross-section construction, the front and rear (i.e. facial, lingual) sides of surface  608  flare outward in an upward direction more than the left and right (i.e. mesial, distal) sides of surface  608 . In particular, the left and right sides of surface  608 , best shown in  FIGS. 119 and 121  extend vertically, parallel to longitudinal axis  602 . In particular, the left and right sides of surface  608 , best shown in  FIGS. 119 and 121  extend vertically, generally parallel to longitudinal axis  602 , but with a slight outward flare in the upward direction providing an angle Q that may be between 1 and 5 degrees. In some configurations, angle Q may be between 0.5 and 10 degrees or between 0.5 and 20 degrees. Thus the length of the minor axis  612  of the upper portion of the elliptical cross-section is equal to the diameter of the cross-section of the circular cross-section of lower portion  606 . The major axis  610  of the elliptical cross-section is greater than the diameter of the circular bottom of the lower portion  606 . To provide a major axis  610  having a greater length, the rear portion of surface  608  of lower portion  606  flares outward at an angle H ( FIG. 118 ) with respect to the longitudinal axis  602 , and the front portion of surface  608  of lower portion  606  flares outward at an angle I with respect to the longitudinal axis  602 . Angles H and I may be constant over the entire height of lower portion  606 , from the bottom surface  614  of abutment  600  to the top  616  of lower portion  606 . Angle H may be between 14 and 21 degrees. Angle I may be between 7 and 13 degrees. Alternatively, angles H and I may be between 10 and 20 or between 0.5 and 20 degrees. 
     Referring to  FIG. 120 , an angle S is defined between upper portion  604  and lower portion  606  of abutment  600 . This angle is between 135 and 170 degrees on the lingual side of the abutment. It is between 135 and 175 degrees on the facial side of the abutment. It is between 115 and 180 degrees on the mesial side and distal side of the abutment. 
     The upper portion  604  of abutment  600  is similar to lower portion  606  in that it has a smooth continuous external surface  618  that is revolved around the longitudinal axis  602  and tapers inwardly over its entire length from the bottom of upper portion  604  to the top of upper portion  604 . The lower end of external surface  618 , like the upper end of external surface  608  is elliptical having a major axis and a minor axis that are substantially the same as the major and minor axes of lower portion  606 . 
     The lower end of upper portion  604  is generally elliptical in axial cross-section. It has a major axis  620  ( FIG. 116 ) and a minor axis  622  that are disposed in the same angular position about longitudinal axis  602  as are major axis  610  and minor axis  612  of lower portion  606 . Thus, when viewing the top or the bottom ( FIGS. 116 ,  117 ) of abutment  600 , the major axes appear superimposed one over the other and likewise the minor axes appear superimposed one over the other. The upper end of lower portion  606  and the lower end of upper portion  604  define ellipses that have major and minor axes of substantially the same length that are disposed in substantially the same location about the longitudinal axis  602  of abutment  600 . 
     Surface  618  tapers inwardly as one traverses surface  618  of upper portion  604  from the lower end of upper portion  604  to the upper end of upper portion  604 . The front portion of surface  618  tapers inwardly at an angle J of 6 degrees ( FIG. 118 ). The rear portion of surface  618  tapers inwardly at an angle K of 6 degrees. In another configuration, angles J and K may be between 6 and 8 degrees. In yet another configuration, angles J and K may be between 0.5 and 10 degrees. The left and right sides of surface  618  taper inwardly at an angle R ( FIG. 119 ) of between 0.5 and 6 degrees. In other configurations R may be between 0.5 and 10 degrees. 
     The top of abutment  600  is defined by three generally planar surfaces: a front surface  624 , a top surface  626 , and a rear surface  628 . These planar surfaces intersect the front, top, and rear portions of surface  618 , forming the upper limits of surface  618 . 
     The intersection  630  of upper portion  604  and lower portion  606  of abutment  600  defines a continuous curving junction line that extends around the entire periphery of abutment  600 . 
     The intersection  630  is highest on the left and right sides of abutment  600  where it reaches two local maxima  632 ,  634  on the right and left sides of abutment  600 , respectively. In one embodiment, illustrated here, local maximum  632  of intersection  630  is higher than local maximum  634  of intersection  630 . 
     The intersection  630  is lowest on the front and the rear of abutment  600  where it reaches two local minima  636 ,  638  at the front and the back sides of abutment  600 , respectively. In one embodiment, illustrated here, local minima  636  of intersection  630  is higher than local minima  638  of intersection  630 . 
     An aperture  640  is provided that extends downward and completely through abutment  600  that is concentric with longitudinal axis  602  and with slightly elliptical bottom surface  614  of abutment  600 . This aperture is best shown in  FIG. 123 , which is a cross-sectional view of abutment  600 . Aperture  640  extends into surfaces  624 ,  626 , and  628  of abutment  600 . Aperture  640  has a constant first diameter L in the upper portion of abutment  600  that extends downward generally to intersection  630 . A chamfer  642  is provided at the bottom of this upper portion of aperture  640 . The lower portion of aperture  640  extends through the bottom of abutment  600  and has a smaller diameter M. This portion of aperture  640  extends approximately from intersection  630  through the bottom surface  614  of abutment  600 . Diameter L may be 2.5 mm and diameter M may be 2 mm in all the implants herein. 
     When the implant is assembled, with abutment  600  inserted into fixture  502 , a threaded fastener (not shown) is inserted into aperture  640  and is threadedly engaged with the threaded portion of the aperture in fixture  502 . The head of the threaded fastener engages chamfer  642  thereby holding the abutment  600  into fixture  502 . 
       FIGS. 163-164  show the fixture  502  and abutment  600  of  FIGS. 116-130  in assembled form as it would exist in the patient&#39;s mouth. The implant  501 , as assembled, includes three components: fixture  502 , abutment  600 , and threaded fastener  700 . 
     The implant is assembled by inserting the lower portion  606  of abutment  600  into hole  540  of fixture  502 . The inside surface of hole  540  is identical in contours to the external surface  608  of lower portion  606 , such that no voids or gaps are provided between the two mating surfaces. The dimensions of the mating surfaces, including cross-sectional areas, degree of ellipticality, diameter of their circular bases, and the various angles at which they flare outward and upward are the same. 
     The inside surface of hole  540  is configured to receive lower portion  606  until lower portion  606  is wedged inside hole  540 . In this position, the longitudinal axis  602  of abutment  600  is coaxial with a longitudinal axis  508  of fixture  502 . Furthermore, threaded hole  548  of fixture  502  is also coaxial with longitudinal axis  602  of abutment  600  as well as coaxial with threaded fastener  700 . 
     The abutment and fixture are sized to ensure that a gap of approximately 0.25 mm remains between the circular bottom  614  of abutment  600  and the circular bottom of hole  540 . This gap ensures that tightening threaded fastener  700  will ensure complete and full frictional engagement of the inside surface of hole  540  and surface  608  of lower portion  606 . 
     The inside surface of hole  540  is configured to receive lower portion  606  until the line that defines the intersection  630  of the outwardly flaring external surface  608  and the inwardly flaring external surface  618  is disposed immediately adjacent to and slightly above the rim of hole  540 . The intersection  630  is disposed axially above the top surface of the fixture a distance of between 0.0 and 1.5 mm around the entire periphery of the implant. This includes on the facial and lingual sides shown in  FIG. 163  (illustrating the minima  636 ,  638  of the intersection  630  disposed this distance above the top surface of the fixture), and on the mesial and distal sides shown in  FIG. 164  (illustrating the maxima  632 ,  634  of the intersection  630  disposed this distance above the top surface of the fixture), and at all places in between. 
     The top surface of the fixture extends radially outward from the intersection  630  a distance of between 0.5 and 1.5 mm around the entire periphery of the implant. This includes on the mesial and distal sides (shown in  FIG. 164 ) and on the facial and lingual sides (shown in  FIG. 163 ) and at all places in between. 
       FIGS. 131-138  are top, bottom, right, back, left, front, perspective, and cross-sectional views, respectively, of abutment  900 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 139-146  are front, cross-sectional, rear, left, top, bottom and perspective views of fixture  802 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 165 ,  166  illustrate the assembled alternative implant  801  comprised of the abutment  900  of  FIGS. 131-138 , the fixture  802  of  FIGS. 139-146 , and a threaded fastener  1000 . In  FIG. 165 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and front-to-rear. In  FIG. 166 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and side-to-side. 
     An identical (but mirror image) implant to the one of  FIGS. 131-146 ,  165 ,  166  can be used to replace central incisor #9. This implant is identical in all respects to implant  801  but in mirror image form and therefore has not been separately illustrated and described herein. 
     Referring now to  FIGS. 139-146 , a dental fixture, here shown as central incisor fixture  802  is illustrated. Fixture  802  includes a lower portion  804  that is formed integral with an upper portion  806 . Fixture  802  includes a longitudinal axis  808  that extends from the lower hemispherical tip  810  of the lower portion  804  to the top of fixture  802 . 
     Lower portion  804  is generally circular in longitudinal cross-section having a smaller diameter at a lower end of portion  804  and a larger diameter at the upper end of portion  804 . Portion  804  is generally conical with an included flare angle of 12 degrees. This angle may be symmetric about the longitudinal axis  808  of the lower portion  804 , such that the cone defined by the major diameter of the threads extends outward from the longitudinal axis  808  by 6 degrees. 
     This taper permits the threads to be progressively wedged into the maxilla or mandible with each successive turn of fixture  802  about its longitudinal axis. As fixture  802  is rotated, it extends deeper into the bone and extends farther outward in a direction normal to the longitudinal axis  808  of fixture  802 , causing each turn of thread  814  to wedge more firmly into the bone. In an alternative arrangement, the fixture can be press fit into the aperture. 
     Lower fixture portion  804  is threaded over substantially all of its length. Thread  814  extends from the upper part of hemispherical tip  810  to the upper end of the threads located generally at the longitudinal midpoint  816  of fixture  802 . 
     Thread  814  has an asymmetric profile, best shown in  FIG. 139 . Thread  814  is a single helical thread that extends the length of lower portion  804  of fixture  802  and has a pitch of 0.576 mm, a depth of 0.5 mm, and a length in an axial direction of 6.0 mm. It flares outward at an angle A of 6 degrees from the longitudinal axis ( FIG. 142 ) as it extends upward. 
     Thread  814  is broken by two longitudinal semi-circular grooves  818 ,  820  that are provided on the outer surface of fixture portion  804 . The grooves are disposed at an angle B of 180 degrees from one another ( FIG. 144 ) as measured in a plane normal to the longitudinal axis  808 . Groove  818  extends vertically along the outer front surface of fixture portion  804 . Groove  820  extends vertically along the outer rear surface of fixture portion  804 . The thread is broken by these grooves (i.e. it does not extend across the grooves). When the fixture is screwed into the bone of the patient&#39;s mouth, grooves  818 ,  820  provide a longitudinally extending void into which bone may grow. Bone that is encouraged to grow into grooves  818 ,  820  prevents the rotation of the fixture when the fixture is twisted about its longitudinal axis. The longitudinally extending voids also permit fluid in the osteotomy in which the fixture is screwed or pressed to escape when the fixture is inserted. 
     The upper portion  806  of fixture  802  is substantially the same length (measured in a longitudinal direction) as lower portion  804 . The outer surface profile of upper portion  806  differs from portion  804 , however. The outer surface  826  of the lower end of upper portion  806  is circular in cross-section with an outer diameter approximately the same as the root diameter of threads  814 . As upper portion  806  extends upward toward its upper end, however, this cross-sectional profile changes from a circular profile to a generally oblate and elliptical profile. The outer surface  828  of the upper end of upper portion  806  is generally elliptical in cross-section. 
     The outer surface  828  has a major axis  830  and a minor axis  832  ( FIG. 143 ), with the major axis  830  extending generally front-to-rear in a facial-to-lingual direction when installed in the patient&#39;s mouth, and minor axis  832  extending generally left-to-right in a mesial-distal direction when installed in the patient&#39;s mouth. 
     When viewed in front view and rear view ( FIGS. 139 ,  141 , respectively), the left and right side walls of upper portion  806  adjacent to thread  814  flare outward in the mesial and distal directions at an angle C that may be between 11 and 13 degrees with respect to the longitudinal axis  808  as they extend upward. About halfway up upper portion  806 , the sidewalls flare inward at a slightly smaller angle D that may be between 3 and 5 degrees with respect to longitudinal axis  808 . 
     When viewed in side view ( FIGS. 140 ,  142 ), the side walls of the upper portion  806  at the left and right ends of the major axis flare outward in the lingual and buccal directions at an angle E of about 21-25 degrees from the longitudinal axis  808  as they extend upward. About halfway up upper portion  806 , the sidewalls extend generally vertically, parallel to the longitudinal axis, although they may be rounded as shown on the upper right hand portion of upper portion  806 . 
     The top surface of the fixture is in the form of two intersecting planar surfaces, a front surface  836 , and a rear surface  838  that are pierced by an irregularly shaped hole  840  extending downward in the axial direction into upper portion  806  of fixture  802 . Surfaces  836 ,  838  intersect to define two local maxima (or peaks)  842 ,  844  of the fixture on the left and right side of the fixture, respectively. These two maxima define the uppermost extent of the fixture on each side. 
     The two surfaces  836 ,  838  of top surface of fixture  802  are radiused or curved where they intersect and do not meet at a sharp line (for example as illustrated in the embodiment of  FIG. 20  in which the front and rear surfaces of the top of the fixture intersect along a line that defines maxima  134 ,  135 ). In the embodiment of  FIGS. 131   139 , this radiused intersection provides two curved crests or peaks (i.e. maxima  842 ,  844 ) located on opposite sides of the top of the fixture. Surfaces  836 ,  838  are not curved to the same degree where they meet. Instead, they are curved more steeply on the left side of the fixture  802  such that the local maximum  842  is slightly higher than the local maximum  844  on the other side of the fixture  802 . 
     Similarly, the two surfaces  836 ,  838  intersect hole  840  at two local minima  841 ,  843  located at the front and back, respectively, of fixture  802 . The rim of hole  840 , where it intersects top surfaces  836 ,  838  defines a continuously curved path around the upper edge of hole  840  between local maxima  842 ,  844  disposed on the left and right sides, respectively, of the fixture  802  and local minima  841 ,  843  located at the front and back, respectively, of fixture  802 . 
     Hole  840  is irregularly shaped, having a cross-sectional profile at its upper end that is substantially elliptical with a major axis extending front to rear and the minor axis extending left to right. As one descends into hole  840 , the hole transitions from a substantially elliptical shape to a substantially circular shape having a diameter that may be less than half the length of the minor axis at the top of the fixture. As one descends into hole  840 , the major axis is reduced in length at a rate greater than the minor axis is reduced in length. In other words, the circular bottom of hole  840  flares outward in a front to rear direction at a rate greater than it flares outward in a side to side direction as one ascends from the bottom of hole  840  to the top of hole  840 . It is this differential rate of flaring that transitions the hole from a circular cross-section at its base to an elliptical cross-section at its upper end. 
     The configuration of hole  840  has several advantages. First, by tapering the hole in this manner, a dental abutment (discussed later herein) can be coupled more firmly to fixture  802  by the wedging effects and the frictional engagement of the external surface  908  of the lower portion of the abutment  900  to the inner wall of hole  840 . Furthermore, by providing hole  840  into an irregular, noncircular longitudinal cross-section over substantially all of its length, the rotation of the abutment with respect to the fixture can be eliminated. Even further, by providing hole  840  with a profile in cross section that has a continuous curve over substantially all of its length (in this case a generally elliptical surface) the sharp corners or other protrusions that serve as anti-rotation structures of  FIGS. 27-31  herein, can be eliminated, and a closer mating between the sidewall of hole  840  and the outer wall of the abutment (discussed below) can be provided as well as a reduction in stress risers by the reduction in sharp transitions (e.g. corners) and the provision of a larger surface area to reduce localized stress. By more closely mating the abutment to hole  840  in the fixture, voids or gaps between the abutment and the fixture can be reduced or eliminated, thus reducing or eliminating the ability for biological matter to accumulate in these voids or gaps and provide a reservoir for infection. This tapering also allows for a greater wall thickness and better force distribution to the bone. 
     Hole  840  has a generally flat bottom ( FIG. 140 ) into which a second threaded hole  848  extends. Hole  848  is smaller in diameter than the bottom of hole  840  and serves to anchor the abutment inserted into hole  840  in place. 
     The sidewall of hole  840  is formed as a smooth continuously curved surface having no sharp transitions such as edges or corners between intersecting planes that could create voids and gaps that accumulate biological matter and provide a reservoir for infection. The cross section of hole  840  is elliptical in cross section at its upper end, and tapers smoothly to a circular cross section at its lower end. The elliptical major axis  850  ( FIGS. 140 ,  143 ) of hole  840  at its upper end is oriented generally front-to-rear (i.e. facial-to-lingual) and its minor axis  852  ( FIGS. 139 ,  143 ) is oriented generally side-to-side (mesial-to-distal). The major and minor axes ( 830 ,  832 ) of the outer surface of the upper portion  806  and the major and minor axes ( 850 ,  852 ) of the hole  840  are generally aligned, but rotationally displaced from each other by an angle G ( FIG. 143 ) of about 35 degrees about the longitudinal axis  808 . 
       FIGS. 131-146  illustrate a dental abutment  900  that is configured to engage the dental fixture illustrated in  FIGS. 139-146 . Dental abutment  900  is an elongate structure having a longitudinal axis  902 . It is formed as a unitary monolithic elongated body that has an upper portion  904  and a lower portion  906 . 
     Lower portion  906  is generally cylindrical and has a smooth continuous external surface  908  that is revolved around the longitudinal axis  902  and tapers outwardly over its entire length from the bottom of lower portion  906  to the top of lower portion  906 . The lower end of lower portion  906  is circular in axial cross-section. The upper end of lower portion  906  is generally elliptical in axial cross-section. The major axis  910  ( FIG. 132 ) of the elliptical cross-section of abutment  900  extends front-to-rear (e.g. facial-to-lingual). The minor axis  912  of the elliptical cross-section of abutment  900  ( FIG. 132 ) extends side-to-side (e.g. mesial-to-distal). 
     In order to achieve this circular cross-section to elliptical cross-section construction, the front and rear (i.e. facial, lingual) sides of surface  908  flare outward in an upward direction more than the left and right (i.e. mesial or distal) sides of surface  908 . In particular, the left and right sides of surface  908 , best shown in  FIGS. 134 and 136  extend vertically, generally parallel to longitudinal axis  902 , but with a slight outward flare in the upward direction providing an angle Q that may be between 3 and 9 degrees. In some configurations, angle Q may be between 0.5 and 10 degrees or between 0.5 and 20 degrees. Thus the length of the minor axis  912  of the upper portion of the elliptical cross-section is slightly greater than the diameter of the circular bottom of lower portion  906 . The major axis  910  of the elliptical cross-section is greater than the diameter of the circular bottom of the lower portion  906 . To provide a major axis  910  having a greater length, the rear portion of surface  908  of lower portion  906  flares outward at an angle H, that may be between 17 and 21 degrees ( FIG. 133 ) with respect to the longitudinal axis  902 , and the front portion of surface  908  of lower portion  906  flares outward at an angle I, that may be between 13 and 19 degrees with respect to the longitudinal axis  902 . Angles H and I may be constant over the entire height of lower portion  906 , from the bottom surface  914  of abutment  900  to the top  916  of lower portion  906 . Alternatively, angles H and I may be between 10 and 20 or between 0.5 and 20 degrees.  
     Referring to  FIG. 135 , an angle S is defined between upper portion  904  and lower portion  906  of abutment  900 . This angle is between 135 and 170 degrees on the lingual side of the abutment. It is between 135 and 175 degrees on the facial side of the abutment. It is between 115 and 180 degrees on the mesial side and distal side of the abutment. 
     The upper portion  904  of abutment  900  is similar to lower portion  906  in that it has a smooth continuous external surface  918  that is revolved around the longitudinal axis  902  and tapers inwardly over its entire length from the bottom of upper portion  904  to the top of upper portion  904 . The lower end of external surface  918 , and the upper end of external surface  908  are elliptical in cross-section having major axes and minor axes that are substantially the same. 
     The lower end of upper portion  904  is generally elliptical in axial cross-section. It has a major axis  920  ( FIG. 131 ) and a minor axis  922  that are disposed in the same angular position about longitudinal axis  902  as are major axis  910  and minor axis  912  of lower portion  906 . Thus, when viewing the top or the bottom ( FIGS. 131 ,  132 ) of abutment  900 , the major axes appear superimposed one over the other and likewise the minor axes appear superimposed one over the other. The upper end of lower portion  906  and the lower end of upper portion  904  define ellipses that have major and minor axes of substantially the same length that are disposed in substantially the same location about the longitudinal axis  902  of abutment  900 . 
     Surface  918  tapers inwardly as one traverses surface  918  of upper portion  904  from the lower end of upper portion  904  to the upper end of upper portion  904 . The front portion of surface  918  tapers inwardly at an angle J, that may be between 5 and 11 degrees. The rear portion of surface  918  tapers inwardly at an angle K, that may be between 5 and 11 degrees. In another configuration, angles J and K may be between 0.5 and 10 degrees. The left and right sides of surface  918  taper inwardly at an angle R ( FIG. 134 ) of between 0.5 and 6 degrees. In other configurations R may be between 0.5 and 10 degrees. 
     The top of abutment  900  is defined by three generally planar surfaces: a front surface  924 , a top surface  926 , and a rear surface  928 . These planar surfaces intersect the front, top, and rear portions of surface  918 , forming the upper limits of surface  918 . 
     The intersection  930  of upper portion  904  and lower portion  906  of abutment  900  defines a continuous curving junction line that extends around the entire periphery of abutment  900 . 
     The intersection  930  is highest on the left and right sides of abutment  900  where it reaches two local maxima  932 ,  934  on the right and left sides of abutment  900 , respectively. In one embodiment, illustrated here, local maximum  932  of intersection  930  is at substantially the same height as local maximum  934  of intersection  930 . 
     The intersection  930  is lowest on the front and the rear of abutment  900  where it reaches two local minima  936 ,  938  at the front and the back sides of abutment  900 , respectively. In one embodiment, illustrated here, local minima  936  of intersection  930  is higher than local minima  938  of intersection  930 . 
     An aperture  940  is provided that extends downward and completely through abutment  900  that is concentric with longitudinal axis  902  and with elliptical bottom surface  914  of abutment  900 . This aperture is best shown in  FIG. 138 , which is a cross-sectional view of abutment  900 . Aperture  940  extends into surfaces  924 ,  926 , and  928  of abutment  900 . Aperture  940  has a constant first diameter L in the upper portion of abutment  900  that extends downward generally to intersection  930 . A chamfer  942  is provided at the bottom of this upper portion of aperture  940 . The lower portion of aperture  940  extends through the bottom of abutment  900  and has a smaller diameter M. This portion of aperture  940  extends approximately from intersection  930  through the bottom surface  914  of abutment  900 . 
     When the implant is assembled, with abutment  900  inserted into fixture  802 , a threaded fastener (not shown) is inserted into aperture  940  and is threadedly engaged with the threaded portion of the aperture in fixture  802 . The head of the threaded fastener engages chamfer  942  thereby holding the abutment  900  into fixture  802 . 
       FIGS. 165-166  show the fixture  802  and abutment  900  of  FIGS. 131-146  in assembled form as it would exist in the patient&#39;s mouth. The implant  801 , as assembled, includes three components: fixture  802 , abutment  900 , and threaded fastener  1000 . 
     The implant is assembled by inserting the lower portion  906  of abutment  900  into hole  840  of fixture  802 . The inside surface of hole  840  is identical in contours to the external surface  908  of lower portion  906 , such that no voids or gaps are provided between the two mating surfaces. The dimensions of the mating surfaces, including cross-sectional areas, degree of ellipticality, diameter of their circular bases, and the various angles at which they flare outward and upward are the same. 
     The inside surface of hole  840  is configured to receive lower portion  906  until lower portion  906  is wedged inside hole  840 . In this position, the longitudinal axis  902  of abutment  900  is coaxial with a longitudinal axis  808  of fixture  802 . Furthermore, threaded hole  848  of fixture  802  is also coaxial with longitudinal axis  902  of abutment  900  as well as coaxial with threaded fastener  1000 . 
     The abutment and fixture are sized to ensure that a gap of approximately 0.25 mm remains between the circular bottom of abutment  900  and the circular bottom of hole  840 . This gap ensures that tightening threaded fastener  1000  will ensure complete and full frictional engagement of the inside surface of hole  840  and surface  908  of lower portion  906 . 
     The inside surface of hole  840  is configured to receive lower portion  906  until the line that defines the intersection  930  of the outwardly flaring external surface  908  and the inwardly flaring external surface  918  is disposed immediately adjacent to the rim of hole  840 . The intersection  930  is disposed axially above the top surface of the fixture a distance of between 0.0 and 1.5 mm around the entire periphery of the implant. This includes on the facial and lingual sides shown in  FIG. 165  (illustrating the minima  936 ,  938  of the intersection  930  disposed this distance above the top surface of the fixture), and on the mesial and distal sides shown in  FIG. 166  (illustrating the maxima  932 ,  934  of the intersection  930  disposed this distance above the top surface of the fixture), and at all places in between. 
     The top surface of the fixture extends radially outward from the intersection  930  a distance of between 0.5 and 1.5 mm around the entire periphery of the implant. This includes on the mesial and distal sides (shown in  FIG. 166 ) and on the facial and lingual sides (shown in  FIG. 165 ) and at all places in between. 
       FIGS. 147-154  are top, bottom, right, back, left, front, perspective, and cross-sectional views, respectively, of abutment  1200 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 155-162  are front, cross-sectional, rear, left, top, bottom and perspective views of fixture  1102 . The cross-sectional view is taken along a cutting plane that extends front to rear and through the longitudinal axis of the abutment. 
       FIGS. 167 ,  168  illustrate the assembled alternative implant  1101  comprised of the abutment  1200  of  FIGS. 147-154 , the fixture  1102  of  FIGS. 155-162 , and a threaded fastener  1300 . In  FIG. 167 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and front-to-rear. In  FIG. 168 , the cutting plane extends through the longitudinal central axis of the implant (the axis of both the fixture and the abutment) and side-to-side. 
     An identical (but mirror image) implant to the one of  FIGS. 147-162 ,  167 ,  168  can be used to replace cuspid #11. This implant is identical in all respects to implant  1101  but in mirror image form and therefore has not been separately illustrated and described herein. 
     Referring now to  FIGS. 155-162 , a dental fixture, here shown as cuspid fixture  1102  is illustrated. Fixture  1102  includes a lower portion  1104  that is formed integral with an upper portion  1106 . Fixture  1102  includes a longitudinal axis  1108  that extends from the lower hemispherical tip  1110  of the lower portion  1104  to the top of fixture  1102 . 
     Lower portion  1104  is generally circular in longitudinal cross-section having a smaller diameter at a lower end of portion  1104  and a larger diameter at the upper end of portion  1104 . Portion  1104  is generally conical with an included flare angle of 12 degrees. This angle may be symmetric about the longitudinal axis  1108  of the lower portion  1104 , such that the cone defined by the major diameter of the threads extends outward from the longitudinal axis  1108  by 6 degrees. 
     This taper permits the threads to be progressively wedged into the maxilla or mandible with each successive turn of fixture  1102  about its longitudinal axis. As fixture  1102  is rotated, it extends deeper into the bone and extends farther outward in a direction normal to the longitudinal axis  1108  of fixture  1102 , causing each turn of thread  1114  to wedge more firmly into the bone. In an alternative arrangement, the fixture can be press fit into the aperture. 
     Lower fixture portion  1104  is threaded over substantially all of its length. Thread  1114  extends from the upper part of hemispherical tip  1110  to the upper end of the threads located generally at the longitudinal midpoint  1116  of fixture  1102 . 
     Thread  1114  has an asymmetric profile, best shown in  FIG. 155 . Thread  1114  is a single helical thread that extends the length of lower portion  1104  of fixture  1102  and has a pitch of 0.576 mm, a depth of 0.5 mm, and a length in an axial direction of 6.0 mm. It flares outward at an angle A of 6 degrees from the longitudinal axis ( FIG. 158 ) as it extends upward. 
     Thread  1114  is broken by two longitudinal semi-circular grooves  1118 ,  1120  that are provided on the outer surface of fixture portion  1104 . The grooves are disposed at an angle B of 180 degrees from one another ( FIG. 160 ) as measured in a plane normal to the longitudinal axis  1108 . Groove  1118  extends vertically along the outer front surface of fixture portion  1104 . Groove  1120  extends vertically along the outer rear surface of fixture portion  1104 . The thread is broken by these grooves (i.e. it does not extend across the grooves). When the fixture is screwed into the bone of the patient&#39;s mouth, grooves  1118 ,  1120  provide a longitudinally extending void into which bone may grow. Bone that is encouraged to grow into grooves  1118 ,  1120  prevents the rotation of the fixture when the fixture is twisted about its longitudinal axis. These grooves also allow for fluid evacuation when press fit into the osteotomy. They also ensure the threads do not come through the facial bone of the maxilla. 
     The upper portion  1106  of fixture  1102  is substantially the same length (measured in a longitudinal direction) as lower portion  1104 . The outer surface profile of upper portion  1106  differs from portion  1104 , however. The outer surface  1126  of the lower end of upper portion  1106  is circular in cross-section with an outer diameter approximately the same as the root diameter of threads  1114 . As upper portion  1106  extends upward toward its upper end, however, this cross-sectional profile changes from a circular profile to a generally oblate and elliptical profile. The outer surface  1128  of the upper end of upper portion  1106  is generally elliptical in cross-section. 
     The outer surface  1128  has a major axis  1130  and a minor axis  1132  ( FIG. 159 ), with the major axis  1130  extending generally front-to-rear in a facial-to-lingual direction when installed in the patient&#39;s mouth, and minor axis  1132  extending generally left-to-right in a mesial-distal direction when installed in the patient&#39;s mouth. 
     When viewed in front view and rear view ( FIGS. 155 ,  157 , respectively), the left and right side walls of upper portion  1106  adjacent to thread  1114  flare outward in the mesial and distal directions at an angle C, that may be between 4 and 9 degrees with respect to the longitudinal axis  1108  as they extend upward. About halfway up upper portion  1106 , the sidewalls flare outward at a slightly smaller angle D, that may be between 0.5 and 11 degrees with respect to longitudinal axis  1108 . 
     When viewed in side view ( FIGS. 156 ,  158 ), the side walls of the upper portion  1106  at the left and right ends of the major axis flare outward in the lingual and buccal directions at an angle E, that may be between 26 and 30 degrees from the longitudinal axis  1108  as they extend upward. About halfway up upper portion  1106 , the sidewalls flare outward at a smaller angle F, that may be between 0.5 and 8 degrees with respect to the longitudinal axis  1108 . 
     The top surface of the fixture is in the form of two intersecting planar surfaces, a front surface  1136 , and a rear surface  1138  that are pierced by an irregularly shaped hole  1140  extending downward in the axial direction into upper portion  1106  of fixture  1102 . Surfaces  1136 ,  1138  intersect to define two local maxima (or peaks)  1142 ,  1144  of the fixture on the left and right side of the fixture, respectively. These two maxima define the uppermost extent of the fixture on each side. 
     The two surfaces  1136 ,  1138  of top surface of fixture  1102  are radiused or curved where they intersect and do not meet at a sharp line (for example as illustrated in the embodiment of  FIG. 20  in which the front and rear surfaces of the top of the fixture intersect along a line that defines maxima  150 ,  151 ). In the embodiment of FIGS.  147 - 155 , this radiused intersection provides two curved crests or peaks (i.e. maxima  1142 ,  1144 ) located on opposite sides of the top of the fixture. Surfaces  1136 ,  1138  are not curved to the same degree where they meet. Instead, they are curved more steeply on the left side of the fixture  1102  such that the local maximum  1142  is higher than the local maximum  1144  on the other side of the fixture  1102 . 
     Similarly, the two surfaces  1136 ,  1138  intersect hole  1140  at two local minima  1141 ,  1143  located at the front and back, respectively, of fixture  1102 . The rim of hole  1140 , where it intersects top surfaces  1136 ,  1138  defines a continuously curved path around the upper edge of hole  1140  between local maxima  1142 ,  1144  disposed on the left and right sides, respectively, of the fixture  1102  and local minima  1141 ,  1143  located at the front and back, respectively, of fixture  1102 . 
     Hole  1140  is irregularly shaped, having a cross-sectional profile at its upper end that is substantially elliptical with a major axis extending front to rear and the minor axis extending left to right. As one descends into hole  1140 , the hole transitions from a substantially elliptical shape to either a substantially circular shape or a substantially elliptical shape (as shown herein) having a diameter that may be less than half the length of the minor axis at the top of the fixture. As one descends into hole  1140 , the major axis is reduced in length at a rate greater than the minor axis is reduced in length. In other words, the circular (or elliptical) bottom of hole  1140  flares outward in a front to rear direction at a rate greater than it flares outward in a side to side direction as one ascends from the bottom of hole  1140  to the top of hole  1140 . It is this differential rate of flaring the transitions the hole from a circular (or smaller elliptical) cross-section at its base to an elliptical cross-section at its upper end. 
     The configuration of hole  1140  has several advantages. First, by tapering the hole in this manner, a dental abutment (discussed later herein) can be coupled more firmly to fixture  1102  by the wedging effects and the frictional engagement of the external surface  1208  of the lower portion of the abutment  1200  to the inner wall of hole  1140 . Furthermore, by providing hole  1140  into an irregular, noncircular longitudinal cross-section over substantially all of its length, the rotation of the abutment with respect to the fixture can be eliminated. Even further, by providing hole  1140  with a profile in cross section that has a continuous curve over substantially all of its length (in this case a generally elliptical surface) the sharp corners or other protrusions that serve as anti-rotation structures of  FIGS. 27-31  herein, can be eliminated, and at closer mating between the sidewall of hole  1140  and the outer wall of the abutment (discussed below) can be provided as well as a reduction in stress risers by the reduction in sharp transitions (e.g. corners) and the provision of a larger surface area to reduce localized stress. By more closely mating the abutment to hole  1140  in the fixture, voids or gaps between the abutment and the fixture can be reduced or eliminated, thus reducing or eliminating the ability for biological matter to accumulate in these voids or gaps and provide a reservoir for infection. This tapering also allows for a greater wall thickness and better force distribution to the bone. 
     Hole  1140  has a generally flat bottom ( FIG. 156 ) into which a second threaded hole  1148  extends. Hole  1148  is smaller in diameter than the bottom of hole  1140  and serves to anchor the abutment inserted into hole  1140  in place. 
     The sidewall of hole  1140  is formed as a smooth continuously curved surface having no sharp transitions such as edges or corners between intersecting planes that could create voids and gaps that accumulate biological matter and provide a reservoir for infection. The cross section of hole  1140  is elliptical in cross section at its upper end, and tapers smoothly to a circular cross section at its lower end. The elliptical major axis  1150  ( FIGS. 156 ,  159 ) of hole  1140  at its upper end is oriented generally front-to-rear (i.e. facial-to-lingual) and its minor axis  1152  ( FIGS. 155 ,  159 ) is oriented generally side-to-side (mesial-to-distal). The major and minor axes ( 1130 ,  1132 ) of the outer surface of the upper portion  1106  and the major and minor axes ( 1150 ,  1152 ) of the hole  1140  are generally aligned, but rotationally displaced from each other by an angle G ( FIG. 159 ) of about 5 degrees about the longitudinal axis  1108 . 
       FIGS. 147-154  illustrate a dental abutment  1200  that is configured to engage the dental fixture illustrated in  FIGS. 155-162 . Dental abutment  1200  is an elongate structure having a longitudinal axis  1202 . It is formed as a unitary monolithic elongated body that has an upper portion  1204  and a lower portion  1206 . 
     Lower portion  1206  is generally cylindrical and has a smooth continuous external surface  1208  that is revolved around the longitudinal axis  1202  and tapers outwardly over its entire length from the bottom of lower portion  1206  to the top of lower portion  1206 . The lower end of lower portion  1206  is generally elliptical in axial cross-section. The upper end of lower portion  1206  is generally elliptical in axial cross-section, but is less elongated than the cross-section at the upper end. The major axis  1210  ( FIG. 148 ) of the elliptical cross-sections of abutment  1200  extend generally front-to-rear (e.g. facial-to-lingual). The minor axis  1212  of the upper and lower elliptical cross-sections of abutment  1200  ( FIG. 148 ) extend generally side-to-side (e.g. mesial-to-distal). 
     In order to achieve this more elongate upper elliptical cross-section to less elongate lower elliptical cross-section construction, the front and rear (i.e. facial, lingual) sides of surface  1208  flare outward in an upward direction more than the left and right (i.e. mesial or distal) sides of surface  1208 . In particular, the left and right sides of surface  1208 , best shown in  FIGS. 150 and 152  extend vertically, generally parallel to longitudinal axis  1202 , but with a slight outward flare in the upward direction providing an angle Q that may be between 1 and 7 degrees. In some configurations, angle Q may be between 0.5 and 10 degrees or between 0.5 and 20 degrees. Thus the length of the minor axis  1212  of the upper elliptical cross-section of lower portion  1206  is slightly greater than the minor axis of the lower elliptical cross-section of lower portion  1206 . The major axis  1210  of the upper elliptical cross-section is greater than the diameter of the elliptical bottom of the lower portion  1206 . To provide a major axis  1210  having a greater length, the rear portion of surface  1208  of lower portion  1206  flares outward at an angle H ( FIG. 149 ) with respect to the longitudinal axis  1202 , and the front portion of surface  1208  of lower portion  1206  flares outward at an angle I with respect to the longitudinal axis  1202 . Angles H and I may be constant over the entire height of lower portion  1206 , from the bottom surface  1214  of abutment  1200  to the top  1216  of lower portion  1206 . Angle H may be between 11 and 18 degrees and angle I may be between 9 and 16 degrees. Alternatively, angles H and I may be between 10 and 20 or between 0.5 and 20 degrees. 
     Referring to  FIG. 149 , an angle S is defined between upper portion  1204  and lower portion  1206  of abutment  1200 . This angle is between 135 and 170 degrees on the lingual side of the abutment. It is between 135 and 175 degrees on the facial side of the abutment. It is between 115 and 180 degrees on the mesial side and distal side of the abutment. 
     The upper portion  1204  of abutment  1200  is similar to lower portion  1206  in that it has a smooth continuous external surface  1218  that is revolved around the longitudinal axis  1202  and tapers inwardly over its entire length from the bottom of upper portion  1204  to the top of upper portion  1204 . The lower end of external surface  1218 , and the upper end of external surface  1208  may have major and minor axes that are substantially the same. 
     The lower end of upper portion  1204  is generally elliptical in axial cross-section. It has a major axis  1220  ( FIG. 147 ) and a minor axis  1222  that are disposed in the same angular position about longitudinal axis  1202  as are major axis  1210  and minor axis  1212  of lower portion  1206 . Thus, when viewing the top or the bottom ( FIGS. 147 ,  148 ) of abutment  1200 , the major axes appear superimposed one over the other and likewise the minor axes appear superimposed one over the other. The upper end of lower portion  1206  and the lower end of upper portion  1204  define ellipses that have major and minor axes of substantially the same length that are disposed in substantially the same location about the longitudinal axis  1202  of abutment  1200 . 
     Surface  1218  tapers inwardly as one traverses surface  1218  of upper portion  1204  from the lower end of upper portion  1204  to the upper end of upper portion  1204 . The front portion of surface  1218  tapers inwardly at an angle J of 6 degrees, or between 3 and 9 degrees. The rear portion of surface  1218  tapers inwardly at an angle K of 6 degrees, or between 3 and 9 degrees. In another configuration, angles J and K may be between 0.5 and 10 degrees. The left and right sides of surface  1218  taper inwardly at an angle R ( FIG. 150 ) of between 0.5 and 6 degrees. In other configurations R may be between 0.5 and 10 degrees. 
     The top of abutment  1200  is defined by three generally planar surfaces: a front surface  1224 , a top surface  1226 , and a rear surface  1228 . These planar surfaces intersect the front, top, and rear portions of surface  1218 , forming the upper limits of surface  1218 . 
     The intersection  1230  of upper portion  1204  and lower portion  1206  of abutment  1200  defines a continuous curving junction line that extends around the entire periphery of abutment  1200 . 
     The intersection  1230  is highest on the left and right sides of abutment  1200  where it reaches two local maxima  1232 ,  1234  on the right and left sides of abutment  1200 , respectively. In one embodiment, illustrated here, local maximum  1232  of intersection  1230  is lower than local maximum  1234  of intersection  1230 . 
     The intersection  1230  is lowest on the front and the rear of abutment  1200  where it reaches two local minima  1236 ,  1238  at the front and the back sides of abutment  1200 , respectively. In one embodiment, illustrated here, local minima  1236  of intersection  1230  is higher than local minima  1238  of intersection  1230 . 
     An aperture  1240  is provided that extends downward and completely through abutment  1200  that is concentric with longitudinal axis  1202  and with elliptical bottom surface  1214  of abutment  1200 . This aperture is best shown in  FIG. 154 , which is a cross-sectional view of abutment  1200 . Aperture  1240  extends into surfaces  1224 ,  1226 , and  1228  of abutment  1200 . Aperture  1240  has a constant first diameter L in the upper portion of abutment  1200  that extends downward generally to intersection  1230 . A chamfer  1242  is provided at the bottom of this upper portion of aperture  1240 . The lower portion of aperture  1240  extends through the bottom of abutment  1200  and has a smaller diameter M. This portion of aperture  1240  extends approximately from intersection  1230  through the bottom surface  1214  of abutment  1200 . 
     When the implant is assembled, with abutment  1200  inserted into fixture  1102 , a threaded fastener (not shown) is inserted into aperture  1240  and is threadedly engaged with the threaded portion of the aperture in fixture  1102 . The head of the threaded fastener engages chamfer  1242  thereby holding the abutment  1200  into fixture  1102 . 
       FIGS. 167-168  show the fixture  1102  and abutment  1200  of  FIGS. 147-162  in assembled form as it would exist in the patient&#39;s mouth. The implant  1101 , as assembled, includes three components: fixture  1102 , abutment  1200 , and threaded fastener  1300 . 
     The implant is assembled by inserting the lower portion  1206  of abutment  1200  into hole  1140  of fixture  1102 . The inside surface of hole  1140  is identical in contours to the external surface  1208  of lower portion  1206 , such that no voids or gaps are provided between the two mating surfaces. The dimensions of the mating surfaces, including cross-sectional areas, degree of ellipticality, diameters of their circular bases (or major and minor axes of their elliptical bases), and the various angles at which they flare outward and upward are the same. 
     The inside surface of hole  1140  is configured to receive lower portion  1206  until lower portion  1206  is wedged inside hole  1140 . In this position, the longitudinal axis  1202  of abutment  1200  is coaxial with a longitudinal axis  1108  of fixture  1102 . Furthermore, threaded hole  1148  of fixture  1102  is also coaxial with longitudinal axis  1202  of abutment  1200  as well as coaxial with threaded fastener  1300 . 
     The abutment and fixture are sized to ensure that a gap of approximately 0.25 mm remains between the elliptical bottom of abutment  1200  and the elliptical bottom of hole  1140 . This gap ensures that tightening threaded fastener  1300  will ensure complete and full frictional engagement of the inside surface of hole  1140  and surface  1208  of lower portion  1206 . 
     The inside surface of hole  1140  is configured to receive lower portion  1206  until the line that defines the intersection  1230  of the outwardly flaring external surface  1208  and the inwardly flaring external surface  1218  is disposed immediately adjacent to the rim of hole  1140 . The intersection  1230  is disposed axially above the top surface of the fixture a distance of between 0.0 and 1.5 mm around the entire periphery of the implant. This includes on the facial and lingual sides shown in  FIG. 167  (illustrating the minima  1236 ,  1238  of the intersection  1230  disposed this distance above the top surface of the fixture), and on the mesial and distal sides shown in  FIG. 168  (illustrating the maxima  1232 ,  1234  of the intersection  1230  disposed this distance above the top surface of the fixture), and at all places in between. 
     The top surface of the fixture extends radially outward from the intersection  1230  a distance of between 0.5 and 1.5 mm around the entire periphery of the implant. This includes on the mesial and distal sides (shown in  FIG. 168 ) and on the facial and lingual sides (shown in  FIG. 167 ) and at all places in between. 
       FIGS. 169 ,  170 , and  171  are facial, bottom (incisal) and lingual views, respectively, of a maxilla having a plurality of embedded implants. These implants include a #6 cuspid implant  1101 , a #7 lateral incisor implant  501 , a #8 central incisor implant  801 , a #9 central incisor implant  801 ′, a #10 lateral incisor implant  501 ′, and a #11 cuspid implant  1101 ′. 
     Implant  1101  is illustrated and described above in  FIGS. 147-160  and (assembled) in  FIGS. 167-168 . Implant  501  is illustrated above in  FIGS. 116-130  and (assembled) in  FIGS. 163-164 . Implant  801  is illustrated above in  FIGS. 131-146  and (assembled) in  FIGS. 165-166 . Implants  1101 ′,  501 ′ and  801 ′ are mirror images of and are configured identically to implants  1101 ,  501 , and  801 , respectively. 
       FIGS. 169-171  illustrate a system of implants held in a predetermined orientation in a patient&#39;s mouth and showing the relative location of each implant with respect to its adjacent implants. In  FIGS. 169-171 , six implants are shown, each of the six being disposed in a healed maxilla—a maxilla in which the bone and soft tissues have grown into and around the implants. Each implant is positioned in a predetermined spatial relationship to the adjacent implants on either side. The implants are placed in osteotomies in the patient&#39;s mouth that are formed in the apertures of missing teeth. Each of the implants  1101 ,  501 ,  801 ,  801 ′,  501 ′,  1101 ′ is placed in a suitably enlarged hole from which a tooth has been removed, either intentionally or accidentally. Thus, their locations correspond to the locations of pre-existing teeth and are disposed in the same positions as those teeth along the curvature of the dental arch of the maxilla. 
     While a system of six implants is described herein, it should be understood that six implants may be used in a single patient&#39;s mouth in order to use the system of implants described herein. However any one or all of the implants from the system may be used. Furthermore, a system of implants may also include more than the six implants shown here. 
     The implants of the system are not placed and oriented accidentally or at random, but are located in known and predetermined positions with respect to each other (i.e. predetermined relative positions), such that the contours and surface features of the implants mimic the contours of the teeth that the implants replace, and the contours and surface features of adjacent implants are in specific predetermined positions with respect to each other. The predetermined relative positions with respect to each other are predetermined relative positions within the preexisting holes. 
     The implants are placed at predetermined positions within the apertures created by the removal of teeth to align the implants with respect to each other in a manner that encourages the growth of soft tissue around the implants in a specific configuration. One does not merely insert an implant until it bottoms out in the hole. Instead, one places an implant in the aperture from which a tooth has been removed, inserts it in that aperture to a predetermined depth that positions it in that aperture relative to an adjacent implant or tooth in a preferred position, and particularly, in the predetermined relative positions described below and illustrated in  FIGS. 169-171 . 
     The predetermined relative position may include a predetermined front to back (facial to lingual) relative position as well as a predetermined relative height (depth) within the implant&#39;s aperture with respect to the adjacent implant or aperture. 
     Each of the implants  1101 ,  501 ,  801 ,  801 ′,  501 ′,  1101 ′ of the system is specially configured to match the characteristics of the tooth it replaces. These characteristics include the mesial/distal width of the tooth it replaces, the facial/lingual width of the tooth it replaces, the contours of the CRJ of the tooth it replaces, and the location of the CRJ of the teeth on either side. 
     Each of the implants  1101 ,  501 ,  801 ,  801 ′,  501 ′,  1101 ′ comprises a fixture with an overall mesial/distal width that is less than the facial/lingual width of that fixture. 
     Each of the implants  1101 ,  501 ,  801 ,  801 ′,  501 ′,  1101 ′ comprises an abutment with an overall mesial/distal width that is less than the facial/lingual width of that abutment. 
     Each of the implants  1101 ,  501 ,  801 ,  801 ′,  501 ′,  1101 ′ comprises a fixture with a top surface having local minima on the lingual and facial sides and local maxima on the mesial and distal sides. 
     When installed in the osteotomies in the patient&#39;s mouth as shown in  FIGS. 169-171 , the local maxima  844  of the two central incisor implants  801 ,  801 ′ are disposed at the same height (i.e. The same incisal position) and maxima  844  are located directly adjacent to each other in the facial-lingual directions. 
     The adjacent maxima  842 ,  544  of the adjacent implant pairs  801 ,  501 , and  801 ′,  501 ′ are offset slightly such that the maxima  544  of implants  501 ,  501 ′ are disposed more cervically along the longitudinal axis of the implant than the maxima  842  of the implants  801 ,  801 ′ and  842 ,  544  are located directly adjacent to each other in the facial-lingual direction (see  FIG. 170 ). 
     The adjacent maxima  542 , 1144  of the adjacent implant pairs  501 ,  1101  and  501 ′,  1101 ′ are offset slightly such that the maxima  542  of implants  501 ,  501 ′ are disposed more cervically along the longitudinal axis of the implant than the maxima  1144  of the implants  1101 ,  1101 ′ and maxima  542 ,  1144  are located directly adjacent to each other in the facial-lingual direction. 
     The overall length of implants  801 ,  801 ′,  1101 ,  1101 ′ in a direction parallel to the longitudinal axis of the implants is greater than the overall length of implants  501 ,  501 ′. 
     The overall width of the implants  501 ,  501 ′ in the lingual-facial direction is less than the overall width of the implants  1101 ,  1101 ′,  801 ,  801 ′ in the lingual-facial direction. 
     The overall width of the implants  501 ,  501 ′ in the mesial-distal direction is less than the overall width of the implants  1101 ,  1101 ′,  801 ,  801 ′ in the mesial-distal direction. 
     The incisal height of implants  501 ,  501 ′ is less than the incisal height of implants  1101 ,  1101 ′,  801 ,  801 ′. 
     Implants  1101 ,  501 ,  801 ,  801 ′,  501 ′, and  1101 ′ are mounted with respect to each other in the maxilla such that the maxima  542 ,  544 ,  842 ,  844 ,  1142 ,  1144  define an arc, indicated by the dash-dot line in  FIG. 170 . This arc substantially follows the curvature of the dental arch of the maxilla. 
     Implants  1101 ,  1101 ′,  801 ,  801 ′ extend farther forward (i.e. in the facial direction) from their maxima than implants  501 ,  501 ′ extend forward from their maxima. Similarly, since the maxima follow the curvature of the dental arch of the maxilla, implants  1101 ,  1101 ′,  801 ,  801 ′ extend farther forward (i.e. in the facial direction) from the curvature of the dental arch of the maxilla than implants  501 ,  501 ′ extend forward from curvature of the dental arch of the maxilla. 
     Having described many alternative embodiments, it will become apparent that various modifications can be made without departing from the scope of the invention as defined in the accompanying claims.