Abstract:
Arrowheads each having a cutting tip defined with a tip body having at least one slot for engageable mounting of a cutting tip blade therein. The tip blades provide a razor sharp cutting edge situated near a forward leading end of the corresponding arrowheads. The tip blade are secured to corresponding tips by holding elements. Some such cutting tips have facets formed thereon. Some such arrowheads are blade-opening arrowheads, whereas other such arrowheads have substantially removably attachable fixed blades disposed therewith, in elongately configured slots upon corresponding arrowhead bodies. The razor sharp cutting edges of the tip blades in conjunction with the corresponding tip bodies and/or facets provide cutting tips of structural integrity so as to sufficiently crush/split heavy bone and push penetrated material easily from its cutting path, while concomitantly slicing soft tissue with the ease of a razors edge.

Description:
BACKGROUND—FIELD OF THE INVENTION 
     This invention relates generally to the forward leading end of devices used for penetrating substances, and more particularly to multi-faceted cutting tips such as the bone splitting cut-on-impact trocar type tips of hunting arrowheads and the cutting tips used in surgical trocars. 
     BACKGROUND—DESCRIPTION OF PRIOR ART 
     Devices having a leading penetrating end used to penetrate a substance are used in many types of applications, including use in archery equipment and surgical instruments. A popular type of penetrating end point or tip that is used both in archery and surgery is the trocar tip. The word trocar has Latin roots of tres meaning three and carre meaning side of a sword or knife. A trocar tip is therefore three sided and is the pointed leading end of an object used to cut or pierce. The three sides of trocar tips are generally hollow ground. The term hollow ground refers to the grinding process used to fabricate the sides of the tip and generally means that the sides are dished-out or substantially concave, as compared to being flat. The hollow ground feature gives the tip better defined cutting edges at the juncture of the sides with each other than the cutting edges at side junctures of tips having flat sides. The hollow ground feature also gives the tip the ability to easily push the substance being penetrated away from the tip. The earliest known use of trocar tips date back to the medieval times where they were used on the leading ends of knights&#39; lances. 
     In surgery a surgical trocar is one type of a surgical instrument that has a leading penetrating end. Surgical trocars are generally used to pierce body cavities during the surgical procedures of dropsy, endoscopy and laparoscopy etc. The penetrating ends of surgical trocars generally have a type of trocar tip, since from such tip they were named. There are various types of surgical trocars, with a variety of different options and accessories available depending on the procedure(s) to be performed. However, the leading end point of the surgical trocar should be as sharp as possible, should push penetrated or cut tissue away from its cutting path, and also should be as cost effective to produce as possible. 
     In archery a bow is used to shoot an arrow towards a target. A conventional arrow has a shaft, a nock at one end that receives the bow string, and an arrowhead or point that attaches to the opposite end of the arrow shaft which aids in penetrating the target. Arrowheads generally have a pointed forward end, and an opposite threaded shaft end that attaches the arrowhead to the arrow shaft. Arrowheads come in a variety of different sizes and configurations depending on their intended use. For example, there are specifically designed arrowheads for competitive target shooting, shooting fish, hunting birds or small game animals, and for hunting big game animals. Arrowheads used for bowhunting are generally know as broadheads. Broadheads have cutting blades and kill game animals by cutting vital organs such as the lungs and vascular vessels such as arteries, which causes rapid hemorrhaging and/or suffocation. Quick and humane kills are dependent on accurate shot placement, and upon the amount or volume of the animal tissue that is cut. Hunting arrowheads that cut more tissue are more lethal, and therefore are better. The volume of tissue that is cut is determined by the cutting diameter of the arrowhead, the number of blades it contains, and by the distance the arrowhead penetrates into the animal. 
     The two most common types of arrowheads used for hunting are fixed-blade arrowheads and blade-opening arrowheads or mechanical arrowheads. Blade-opening arrowheads differ from conventional fixed-blade arrowheads in that the cutting blades are folded up or held adjacent to the arrowhead body in a retracted position while the arrow is in flight, but at impact with the game animal rotate or pivot into an open position, whereas the blades of fixed-blade arrowheads are permanently held at a full cutting diameter position at all times. 
     Both blade-opening and fixed-blade arrowheads have a pointed tip end used for penetrating the game animal. The tip of the arrowhead may be separably attachable to the arrowhead body or may be integral with it. Conventional arrowheads have historically had two basic types of pointed arrowhead tips: bone-crushing chisel type tips such as the hollow ground trocar tip, and razor blade type tips. The razor blade tips are generally just an extension of the cutting blades of the arrowhead and terminate in a leading pointed apex. Both types of arrowhead tips are designed to maximize penetration and therefore provide a more lethal arrowhead by cutting a larger volume of animal tissue. Despite their designs and intent both the bone crushing chisel tips and the razor blade tips fall short of providing optimum penetrating performance. Since the arrowhead razor blade type tips generally have a true cutting edge, or a cutting edge that has a small enough angle between opposing sides so as to make it as sharp as a razor or scalpel blade, they penetrate the best through soft tissues such as skin, muscles, lungs and other internal organs by slicing or cutting. But when a razor blade tip impacts bone the thin cutting blade generally gets sheared or broken-off due to the heavy impact forces delivered to it, and thus leaves a blunt snagging leading end that greatly inhibits penetration and therefore is less lethal in many instances —since arrowheads very commonly impact bone when penetrating game animals. The bone-crushing chisel tips on the other hand split right through heavy bone but lack a truly sharp cutting edge and therefore do not perform as well in penetrating the skin and other soft tissues. 
     Attempts in the prior art have been made to combine a scalpel sharp cutting edge with bone splitting capabilities into an optimally penetrating arrowhead tip, but these attempts have their own problems as well. For example the introduction of chisel tips with hollow ground sides, such as the three sided trocar tip for arrowhead points helped reduce the angle of the cutting edge between the sides of the tip. But the edges of conventional trocar arrowhead tips and other hollow ground arrowhead tips are still relatively dull and are a far cry from having the fine cutting angle or edge a scalpel or razor blade possesses. Other attempts in the prior art to increase the sharpness of the edges of chisel type arrowhead tips have been made by increasing the curvature of the hollow ground sides. This practice greatly weakens the tip giving it problems similar to those of the razor blade type tips and also provides a tip that does not push the tissue away from the arrowhead optimally. 
     It is apparent that there are needed improvements in cutting tips. 
     It is apparent that there is a need for an arrowhead cutting tip that combines the optimal penetration features of the most rugged bone splitting trocar or chisel type arrowhead tips with the razor sharp cutting features of the razor blade type arrowhead tips into one arrowhead tip. 
     It is also apparent that there is a need for a cutting tip of a surgical trocar that is cost effective to produce, extremely sharp, and that pushes the penetrated or cut tissue away from its cutting path. 
     SUMMARY OF THE INVENTION 
     It is one object of the present invention to provide cutting tips and penetrating tips that cut and/or penetrate more efficiently than prior art cutting tips. 
     It is another object of the present invention to provide a cutting tip that has a smaller angle as referenced between cutting tip structure such as adjoining sides or facets that are located a distance closer to their respective cutting edge than an angle as referenced between cutting tip structure such as adjoining sides or facets located a distance further from the respective cutting edge than the first or closer distance, as measured in the same perpendicular plane to the central longitudinal axis of the respective cutting tip. 
     It is another object of the present invention to provide a cutting tip that has a side or facet with a cutting edge from which for at least a portion of the time that the cutting edge of the facet is being formed, facet material is removed from only the bisected side of the facet that the cutting edge being formed is on. 
     It is another object of the present invention to provide a cutting tip that has a side or facet that is formed at least in part from a rotational grinding wheel whose axis of rotation is inclined with respect to the central longitudinal axis of the cutting tip when forming at least a portion of the facet. 
     It is another object of the present invention to provide a cutting tip that has a side or facet with a facet bisecting plane, wherein the facet is formed at least in part from a rotational grinding wheel whose axis of rotation is inclined with respect to the bisecting plane of the facet when forming at least a portion of the facet. 
     It is another object of the present invention to provide a cutting tip having a central longitudinal axis that is collinear with the Y-axis of a Cartesian X-Y-Z axis system, and a side or facet that is formed from a plurality of rotational machining tools -such as grinding wheels-each having an axis of rotation where the axis of rotation of at least one rotational machining tool of the plurality of rotational machining tools is oriented, with respect to at least one of the X-Y-Z axises and therefore at least one of the corresponding three dimensional planes X-Y, X-Z and Y-Z when forming its particular portion of the facet or cutting tip, in a different manner or spatial orientation than the spatial orientation the axis of rotation of at least one other rotational machining tool of the plurality of rotational machining tools when the other rotational machining tool is forming its particular portion of the facet or cutting tip. 
     It is another object of the present invention to provide a cutting tip that has a side or facet that is formed from a plurality of rotational machining tools each having a radius of rotation where at least one rotational machining tool of the plurality of rotational machining tools has a radius of rotation that has a different length of radius than the radius of rotation of at least one other rotational machining tool. 
     It is another object of the present invention to provide a cutting tip that has a side or facet that is formed from a plurality of rotational machining tools each having an axial thickness where at least one rotational machining tool of the plurality of rotational machining tools has a different axial thickness than the axial thickness of at least one other rotational machining tool. 
     It is another object of the present invention to provide a cutting tip that has a side or facet that is formed from a plurality of rotational machining tools each having an exterior circumferential profile where at least one rotational machining tool of the plurality of rotational machining tools has a different exterior circumferential profile than the exterior circumferential profile of at least one other rotational machining tool. 
     It is also another object of the present invention to provide a cutting tip whose barrel portion has a razor sharp cutting edge. 
     It is also another object of the present invention to provide a cutting tip which has tip blades. 
     It is also another object of the present invention to provide a blade-opening arrowhead having blades that pivot in a rearward direction away from the tip of the arrowhead, which has a razor sharp cutting tip to enhance penetration. 
     It is still another object of the present invention to provide a faceted cutting tip of a surgical trocar that is cost effective to produce, extremely sharp, and that pushes the penetrated or cut tissue away from its cutting path. 
     It is yet further another object of the present invention to provide an arrowhead cutting tip that combines the optimal penetration features of the most rugged bone splitting trocar or chisel type arrowhead tips with the razor sharp cutting features of the razor blade type arrowhead tips into one arrowhead tip. 
     The foregoing objects and advantages and other objects and advantages of the present invention are accomplished as according to one preferred embodiment of this invention with a three faceted hollow ground stainless steel cutting tip that has a bevel ground on each facet adjacent to and communicating with each cutting edge which is located at each facet juncture with an adjacent facet, such that the angle between the bevel of one facet and the facet on the side of the cutting edge opposite the facet with the bevel thereon is less than an angle measured between points located a distance from the cutting edge that is beyond the bevel or further from the cutting edge than the bevel. Such a cutting tip is preferably formed by first grinding the three hollow ground facets with a specific grinding wheel, and then by grinding each of the three bevels on the hollow ground facets with a different grinding wheel. Such a cutting tip enables the formation of an extremely sharp cutting edge at each facet juncture, such as that is attainable on a scalpel blade or a razor blade, while retaining the facet structure necessary to optimally push penetrated material away from the cutting tip and to easily split and crush heavy bone. Such a cutting tip would in effect combine the optimal penetration features of the most rugged bone splitting trocar or chisel type arrowhead tips with the razor sharp cutting features of the razor blade type arrowhead tips into one arrowhead tip, and thus create a deep penetrating and ultimately tough and lethal trocarazor or trocrazor arrowhead tip. 
     Another preferred embodiment according to this invention differs from the above described embodiment in that there are two bevels formed upon each facet so that each cutting edge has a bevel on either side of it. 
     Other preferred embodiments according to this invention have razor sharp cutting edges located on the barrel portion of each cutting tip, or the portion of the cutting tip reward of the facets. According to some such embodiments the cutting tips may have both razor sharp edges located upon the barrel section of the tips and also at the facet junctures. 
     Yet other preferred embodiments according to this invention differ from the above described embodiments in that the razor sharp edges are attained by attachment of separate razor blades or tip blades to the cutting tips by inserting them into slots in the cutting tip body. According to some such preferred embodiments the tip blades are integrally attached to the tip body, such as by welding. According to other such preferred embodiments the attachable tip blades are removably attachable. 
     Yet still other preferred embodiments according to the cutting tips of this invention differ from the above described embodiments in that the facets are flat or convex, or that the cutting tips have differing numbers of facets or differing shapes, may be made of different materials, may have friction reducing elements applied thereto such as polytetrafloroethylene (PTFE), and may have different numbers of cutting edges associated therewith. 
     The cutting tips according to this invention overcome deficiencies inherit in prior art cutting tips. The cutting tips according to this invention have sharper edges while retaining optimal strength and optimal material pushing capabilities. The cutting tips as according to this invention provide for a more lethal arrowhead tip that is capable of deeper penetration than prior art arrowhead tips. The cutting tips according to this invention are also simple and feasible to manufacture. 
     With the above objects and advantages in view, other objects and advantages of the invention will more readily appear as the nature of the invention is better understood, the invention is comprised in the novel construction, combination and assembly of parts hereinafter more fully described, illustrated, and claimed. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a side view of a cutting tip according to one preferred embodiment of this invention; 
     FIG. 2 is another side view of the cutting tip of FIG. 1; 
     FIG. 3 is a top view of the cutting tip of FIG. 1; 
     FIG. 4 is a cross-sectional view of the cutting tip of FIG. 1 taken along line  4 — 4 ; 
     FIG. 5 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 4; 
     FIG. 6 is a side view of a fixed-blade arrowhead with a cutting tip according to a preferred embodiment of this invention; 
     FIG. 7 is a side view of a blade-opening arrowhead with a cutting tip according to a preferred embodiment of this invention, showing the pivotal blades in the closed position; 
     FIG. 8 is a side view of the blade-opening arrowhead as illustrated in FIG. 7 showing the pivotal blades in the open position; 
     FIG. 9 is a side view of a blade-opening arrowhead similar to the blade-opening arrowhead as illustrated in FIGS. 7 &amp; 8 except the cutting tip is integral with the arrowhead body. 
     FIG. 10 is a side view of a surgical trocar with a removably attachable cutting tip as according to a preferred embodiment of this invention; 
     FIG. 11 is a side view of another surgical trocar with an integral cutting tip as according to a preferred embodiment of this invention; 
     FIG. 12 is a side view of a three faceted hollow ground cutting tip; 
     FIG. 13 is a top view of the cutting tip as illustrated in FIG. 12; 
     FIG. 14 is a side view of a grinding wheel; 
     FIG. 15 is an illustration of the three dimensions as depicted with a Cartesian X-Y-Z axis system; 
     FIG. 16 is a top view of the cutting tip as illustrated in FIG. 13 showing a grinding wheel grinding a bevel on the cutting tip; 
     FIG. 17 is a side view of the cutting tip and grinding wheel as illustrated in FIG. 16; 
     FIG. 18 is a side view of another grinding wheel; 
     FIG. 19 is a side view of another grinding wheel; 
     FIG. 20 is a side view of another three faceted hollow ground cutting tip; 
     FIG. 21 is a top view of the cutting tip as illustrated in FIG. 20; 
     FIG. 22 is a side view of another grinding wheel; 
     FIG. 23 is an illustration of the three dimensions as depicted with a Cartesian X-Y-Z axis system; 
     FIG. 24 is a top view of the cutting tip as illustrated in FIG. 21 showing a grinding wheel grinding a bevel on the cutting tip; 
     FIG. 25 is a side view of the cutting tip and grinding wheel as illustrated in FIG. 24; 
     FIG. 26 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 27 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 26; 
     FIG. 28 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 29 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 28; 
     FIG. 30 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 31 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 30; 
     FIG. 32 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 33 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 32; 
     FIG. 34 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 35 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 34; 
     FIG. 36 is a side view of another cutting tip as according to this invention; 
     FIG. 37 is another side view of the cutting tip as illustrated in FIG. 36; 
     FIG. 38 is a top view of the cutting tip as illustrated in FIG. 36; 
     FIG. 39 is a cross-sectional view of the cutting tip as illustrated in FIG. 36 taken along line  39 — 39 ; 
     FIG. 40 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 39; 
     FIG. 41 is a side view of another cutting tip as according to this invention; 
     FIG. 42 is another side view of the cutting tip as illustrated in FIG. 41; 
     FIG. 43 is a top view of the cutting tip as illustrated in FIG. 41; 
     FIG. 44 is a cross-sectional view of the cutting tip as illustrated in FIG. 42 taken along line  44 — 44 ; 
     FIG. 45 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 44; 
     FIG. 46 is a side view of a fixed-blade arrowhead with a cutting tip according to a preferred embodiment of this invention; 
     FIG. 47 is a side view of a blade-opening arrowhead with an integral cutting tip according to a preferred embodiment of this invention, showing the pivotal blades in the open position; 
     FIG. 48 is a side view of a surgical trocar with a removably attachable cutting tip as according to a preferred embodiment of this invention; 
     FIG. 49 is a side view of another surgical trocar with an integral cutting tip as according to a preferred embodiment of this invention; 
     FIG. 50 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 51 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 50; 
     FIG. 52 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 53 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 51; 
     FIG. 54 is a side view of another cutting tip as according to a preferred embodiment of this invention showing a hone bevel; 
     FIG. 55 is a cross-sectional view of the cutting tip as illustrated in FIG. 54 taken along line  55 — 55 ; 
     FIG. 56 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 55; 
     FIG. 57 is an enlarged view of a cutting edge from the cross-sectional view of another cutting tip as according to this invention showing another hone bevel; 
     FIG. 58 is an enlarged view of a cutting edge from the cross-sectional view of another cutting tip as according to this invention showing another hone bevel; 
     FIG. 59 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 60 is an enlarged view of a cutting edge from the cross-sectional view of FIG. 59; 
     FIG. 61 is a side view of another cutting tip as according to this invention; 
     FIG. 62 is another side view of the cutting tip as illustrated in FIG. 61; 
     FIG. 63 is a top view of the cutting tip as illustrated in FIG. 61; 
     FIG. 64 is a cross-sectional view of the cutting tip as illustrated in FIG. 61 taken along line  64 — 64 ; 
     FIG. 65 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 66 is a side view of another cutting tip as according to this invention; 
     FIG. 67 is a cross-sectional view of the cutting tip as illustrated in FIG. 66 taken along line  67 — 67 ; 
     FIG. 68 is an exploded side view of the cutting tip as according to the preferred embodiment of this invention as illustrated in FIG. 66 showing the cutting tip with the tip blades removed; 
     FIG. 69 is a side view of another cutting tip as according to this invention; 
     FIG. 70 is a top view of the cutting tip as illustrated in FIG. 69; 
     FIG. 71 is a cross-sectional view of the cutting tip as illustrated in FIG. 69 taken along line  71 — 71 ; 
     FIG. 72 is a cross-sectional view of the cutting tip as illustrated in FIG. 69 taken along line  72 — 72 ; 
     FIG. 73 is a side view of another cutting tip as according to this invention; 
     FIG. 74 is a cross-sectional view of the cutting tip as illustrated in FIG. 73 taken along line  74 — 74 ; 
     FIG. 75 is a cross-sectional view of the cutting tip as illustrated in FIG. 73 taken along line  75 — 75 ; 
     FIG. 76 is an exploded side view of the cutting tip as according to the preferred embodiment of this invention as illustrated in FIG. 73 showing the cutting tip with the tip blades removed; 
     FIG. 77 is a side view of another cutting tip as according to this invention; 
     FIG. 78 is a top view of the cutting tip as illustrated in FIG. 77; 
     FIG. 79 is a top view of another cutting tip as according to this invention; 
     FIG. 80 is a top view of another cutting tip as according to this invention; 
     FIG. 81 is a top view of another cutting tip as according to this invention; 
     FIG. 82 is a side view of another cutting tip as according to this invention; 
     FIG. 83 is a top view of the cutting tip as illustrated in FIG. 82; 
     FIG. 84 is an exploded side view of the cutting tip as illustrated in FIG. 82 showing two tip blades detached from the cutting tip; 
     FIG. 85 is a side view of a blade-opening arrowhead with a cutting tip as according to a preferred embodiment of this invention, showing the pivotal blades in the open position; 
     FIG. 86 is a side view of another blade-opening arrowhead similar to the blade-opening arrowhead as illustrated in FIG. 85 except for the cutting tip is integral with the arrowhead body. 
     FIG. 87 is a cross-sectional view of the cutting tip as illustrated in FIG. 86 taken along line  87 — 87 ; 
     FIG. 88 is a cross-sectional view of another cutting tip as according to this invention; 
     FIG. 89 is an exploded side view of an arrowhead body and cutting tip as according to this invention; 
     FIG. 90 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 89; 
     FIG. 91 is a side view of another tip blade as according to a preferred embodiment to this invention; 
     FIG. 92 is an exploded side view of an arrowhead body and cutting tip as according to this invention; 
     FIG. 93 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 92; 
     FIG. 94 is a side view of an arrowhead body and cutting tip as according to this invention; 
     FIG. 95 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 94; 
     FIG. 96 is a perspective view of the tip blade as illustrated in FIGS. 94 &amp; 95; 
     FIGS. 97 a-c  show other tip blades as according to other preferred embodiments of this invention; 
     FIG. 98 is a side view of an arrowhead body and cutting tip as according to this invention; 
     FIG. 99 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 98; 
     FIG. 100 is a side view of an arrowhead body and cutting tip as according to this invention; 
     FIG. 101 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 100; 
     FIG. 102 shows another tip blade as according to another preferred embodiment of this invention; 
     FIG. 103 is a side view of a fixed-blade arrowhead with a cutting tip as according to a preferred embodiment of this invention; 
     FIG. 104 is a top view of the fixed-blade arrowhead as illustrated in FIG. 103; 
     FIG. 105 is an exploded side view of the arrowhead body and cutting tip of the arrowhead as illustrated in FIG. 103; 
     FIG. 106 is a partially sectioned side view of the assembled arrowhead components as illustrated in FIG. 105; 
     FIG. 107 is a side view of another fixed-blade arrowhead blade according to another preferred embodiment of this invention; 
     FIG. 108 is a top view of another fixed-blade arrowhead having a cutting tip as according to another preferred embodiment of this invention; 
     FIG. 109 is a partially sectioned side view of the arrowhead body and cutting tip as according to the preferred embodiment of this invention as illustrated in FIG. 108; 
     FIG. 110 is a side view of a tip blade of the cutting tip of the fixed-blade arrowhead of this invention as illustrated in FIGS. 108 &amp; 109; 
     FIG. 111 is an exploded side view of another cutting tip as according to this invention; 
     FIG. 112 is a side view of another cutting tip as according to this invention; 
     FIG. 113 is a cross-sectional view of the cutting tip as illustrated in FIG. 112 taken along line  113 — 113 ; 
     FIG. 114 is a top view of another cutting tip as according to this invention; 
     FIG. 115 is a side view of the cutting tip of this invention as illustrated in FIG. 114; 
     FIG. 116 is a top view of another cutting tip as according to this invention; 
     FIG. 117 is a side view of the cutting tip of this invention as illustrated in FIG. 116; and 
     FIGS. 118-131 are cross-sectional views of yet other cutting tips as according to this invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIGS. 1-5 illustrate a preferred embodiment of this invention, wherein a cutting tip  200  has three hollow ground facets  400 - 400 - 400 . Each facet  400  is ground upon a barrel section  900  of cutting tip  200 . Cutting tip  200  tapers to a pointed apex  376  at its forward leading end as illustrated in FIG.  1 . Each facet  400  has a bevel  500  ground thereon. Bevels  500 - 500 - 500  create a sharper cutting edge  300  at the facet junctures of cutting tip  200  than is attainable by a conventional trocar tip having only hollow ground facets, while allowing cutting tip  200  to retain sufficient structural facet strength to crush/split heavy bone and easily push penetrated material from its cutting path. Each facet  400  has a pair of facet boundaries. Each facet boundary is defined by a cutting edge  300  where a facet  400  adjoins an adjacent facet  400 . A facet  400  and other facets of the other preferred cutting tip embodiments of this invention is therefore generally defined as the cutting tip structure between the pair of facet boundaries or cutting edges of the respective facet. Therefore each bevel is part of its accompanying facet. Each bevel  500  creates a bevel boundary  600  upon its corresponding facet  400 . Each bevel boundary  600  marks the location on each facet  400  where the slope of the corresponding facet  400  changes, as is readily determined by observation of a cross-sectional view of cutting tip  200  such as is illustrated in FIG.  4 . The cross-sectional views of cutting tip  200  as shown in FIGS. 4 &amp; 5 are taken in a plane perpendicular to a central longitudinal axis  1010  of cutting tip  200 . Central longitudinal axis  1010  is collinear with the Y-axis of a Cartesian X-Y-Z axis system as illustrated in FIGS. 1 &amp; 4. A facet bisecting plane  660  as also illustrated in FIGS. 1 &amp; 4 bisects each facet  400  into two longitudinal halves. Each bevel  500  of cutting tip  200  is substantially on only one bisected side of its corresponding facet  400 . As illustrated in FIG. 1 bevel  500  is on the right side of corresponding bisecting plane  660 . As also illustrated in FIG. 1 facet bisecting plane  660  is coplanar with the Y-Z plane (coming out of the page). 
     As illustrated in FIG. 5 an enlarged cross-sectional view of one of the cutting edges  300  of cutting tip  200  clearly shows that a proximal angle  670  has an angle of measure that is less than the angle of measure of a distal angle  672  which therefore gives each cutting edge  300  of cutting tip  200  a true cutting edge and therefore its razor or scalpel sharpness, while retaining the optimally desired facet structure. A true cutting edge is a cutting edge that has a small enough angle between opposing structure such as facets or sides so as to make it as sharp as a razor blade or scalpel blade. It is within the desired results of this invention to provide cutting tips, such as three faceted hollow ground trocar tips that have such a true cutting edge located at each facet juncture. However, it is apparent that obtaining such a fine or small angle so as to produce a true cutting edge between opposing facets or other structures of the cutting tips as according to this invention is not of necessity a requirement for all cutting tips as according to this invention, but rather the creation of a finer or sharper edge than prior art cutting tips possess at their facet junctures and/or at their other structural sections. Proximal angle  670  has preferably an angular measure of between 10 and 35 degrees, but is not intended to be limited thereto. Proximal angle  670  is determined by measuring the angle in a plane perpendicular to central longitudinal axis  1010  of cutting tip  200  between a pair of proximal angle measuring reference points  1000  &amp;  1002  and cutting edge  300 . Distal angle  672  is determined by measuring the angle in the same perpendicular plane to central longitudinal axis  1010  of cutting tip  200  between a pair of distal angle measuring reference points  1004  &amp;  1006  and cutting edge  300 . 
     It is apparent that the method of determining the angle that adjoining facets, bevels or their equivalents are offset from each other with respect to the shape of their corresponding cutting tips and cutting edges as according to this invention may not have to be referenced from the corresponding cutting edge it self. 
     Proximal angle  670  and other proximal angles or their equivalents as according to the desired results of this invention which create an angle of measure that is less than distal angle  672  or other similar corresponding distal angles or their equivalents as according to this invention may be any angle that has angle measuring reference points located a distance from their corresponding cutting edge less than the distance their corresponding bevel boundary is from the cutting edge, as referenced in a plane perpendicular to the central longitudinal axis of the respective cutting tip. Distal angle  672  and other distal angles or their equivalents as according to the desired results of this invention which create an angle of measure that is greater than proximal angle  670  or other similar proximal angles or their equivalents as according to this invention therefore may be any angle that has angle measuring reference points located a distance from their corresponding cutting edge not less than the distance their corresponding bevel boundary is from the cutting edge, as referenced in a plane perpendicular to the central longitudinal axis of the respective cutting tip. 
     It is apparent that each point of a pair of angle measuring reference points used to determine the angle of measure, and therefore the angular offset of opposing cutting tip structural sections, whether a proximal angle or a distal angle as according to this invention, need not necessarily be the same distance from their corresponding cutting edge. 
     FIGS. 6-11 illustrate examples of types of devices that have a leading penetrating end used for penetrating substances which cutting tip  200  or other cutting tips as according to this invention can be associated with as according to the scope of this invention. FIG. 6 illustrates a fixed-blade arrowhead  702  that has cutting blades  722 - 722 - 722  and cutting tip  200  removably attached to an arrowhead body  732 . FIGS. 7 &amp; 8 illustrate a blade-opening arrowhead  700  that has pivotal cutting blades  720 - 720 - 720  and cutting tip  200  removably attached to an arrowhead body  730 . FIG. 7 shows pivotal blades  720 - 720 - 720  in the closed or in-flight position, whereas FIG. 8 shows pivotal blades  720 - 720 - 720  in the open cutting position. FIG. 9 shows a blade-opening arrowhead  704  similar to blade-opening arrowhead  700  as illustrated in FIGS. 7 &amp; 8 except for a cutting tip  204  is integrally attached with an arrowhead body  731 . FIG. 10 illustrates a surgical trocar  706  that has a cannula  740  or trocar tube, a mandrel shank  744  or trocar obturator shank with cutting tip  200  removably attached thereto. FIG. 11 illustrates another surgical trocar  708  similar to surgical trocar  706  except for a cutting tip  202  is integrally attached with a mandrel shank  742 . 
     The cutting tips according to this invention are preferably fabricated from metal stock material such as 400 series stainless steels, titanium alloys—including beta alloys, ferrous steels and carbides, but may be fabricated in their entirety or in part from other metals and non-metals such as organic polymers, composites or any combination of such materials or any other plausible materials. 
     It is apparent that friction reducing elements such as polytetrafloroethylene (PTFE) may be applied to the cutting tips of this invention, especially to the cutting tips fabricated of metal, to enhance their penetrating qualities. 
     FIGS. 12-17 illustrate in part a method of manufacturing cutting tip  200 . FIG. 12 shows a conventional three faceted hollow ground trocar tip, that had its facets  400 - 400 - 400  ground by a grinding wheel  800  as illustrated in FIG.  14 . Grinding wheel  800  has a radius of rotation  804 , an axial thickness  802  and an exterior circumferential profile  836 . Grinding wheel  800  is a type of rotational machining tool as according to this invention, because it rotates about an axis or spins and when shaping or forming objects. Other rotational machining tools as according to this invention comprise mill cutter heads, sanding wheels and any other type of shape forming device that rotates around at least one axis. In FIG. 14 radius of rotation  804  is depicted as the greatest radius of grinding wheel  800 , but it is apparent that the radius of rotation  804  of grinding wheel  800  and the radiuses of rotation of other grinding wheels and rotational machining tools as according to this invention may be any actual radial length possessed by the rotational machining tool or grinding wheel, since such grinding wheels and/or rotational machining tools may have changing radial lengths throughout their axial thickness as does grinding wheel  800 . The exterior circumferential profile of a rotational machining tool of this invention refers to surface shape of the part of the rotational machining tool that is actually contacting the object being formed, manufactured or ground. Although grinding wheel  800  forms each hollow ground facet  400  of cutting tip  200  by exterior circumferential profile  836  section of grinding wheel  800  removing cutting tip stock material during the grinding process, it is apparent that a section  837  of grinding wheel  800  could be used to grind or fabricate a facet, particularly a flat facet, of a cutting tip as according to this invention wherein section  837  would be an exterior circumferential profile. 
     FIG. 13 illustrates that the axis of rotation  1008  of grinding wheel  800 , when grinding wheel  800  is grinding a facet  400  upon cutting tip  200 , is substantially parallel to central longitudinal axis  1010  or the Y-axis, and is perpendicular to both the X-axis and Z-axis. Axis of rotation  1008  of grinding wheel  800 , when grinding wheel  800  is grinding each facet  400  upon cutting tip  200 , is therefore not inclined relative to any of the X, Y, or Z axises nor any of the three dimensions—their corresponding two dimensional planes; X-Z, X-Y, Y-Z. The term inclined as according to this invention has the intended meaning of being neither perpendicular nor parallel. 
     Axis of rotation  1008  of grinding wheel  800  when grinding wheel  800  is grinding each facet  400  upon cutting tip  200 , is orientated with respect to the X-Y-Z axis system of cutting tip  200  in a specific spatial orientation. A spatial orientation as according to this invention refers to the three-dimensional occupancy of space, and particularly to the three-dimensional occupancy of space that axises of rotation of grinding wheels and/or rotational machining tools are oriented with respect to a corresponding Cartesian X-Y-Z axis system of a corresponding cutting tip. 
     FIGS. 16 &amp; 17 show another grinding wheel  806  grinding a bevel  500  upon one of the facets  400  after grinding wheel  800  formed facets  400 - 400 - 400 . Grinding wheel  806  has a radius of rotation  810 , an axial thickness  808  and an exterior circumferential profile  838 . The radius of rotation  810  of grinding wheel  806  is of a different length of radius than the radius of rotation  804  of grinding wheel  800 . The axial thickness  808  of grinding wheel  806  is of a different thickness than the axial thickness  802  of grinding wheel  800 . The exterior circumferential profile  838  of grinding wheel  806  is also of a different profile than the exterior circumferential profile  836  of grinding wheel  800 . 
     As is illustrated in FIGS. 16 &amp; 17 the axis of rotation  1012  of grinding wheel  806  is inclined relative to each of the X, Y, and Z axises of a Cartesian X-Y-Z axis system and therefore also inclined to the corresponding X-Y, X-Z, and Y-Z planes when grinding wheel  806  is forming each bevel  500  upon cutting tip  200 . Therefore, the axis of rotation  1012  of grinding wheel  806  when forming a bevel  500  upon a particular facet  400  of cutting tip  200  is oriented with respect to at least one of the X-Y-Z axises and corresponding three dimensional planes in a different relation or spatial orientation than the spatial orientation axis of rotation  1008  of grinding wheel  800  is oriented with respect to the X-Y-Z axises and three dimensional planes when forming the particular portion of the facet—the primary structure or the hollow ground facets. Each bevel  500  is substantially on only one bisected side of its corresponding facet  400 , thus grinding wheel  806  when forming a bevel  500  upon a facet  400  is removing facet material or cutting tip stock material from only one bisected side of that facet  400  for a substantial majority of the time that grinding wheel  806  is forming the particular bevel  500 . This is clearly illustrated in FIG. 16 where the bevel  500  grinding wheel  806  is shown forming is substantially completely on the right side of facet bisecting plane  660 , which bisecting plane  660  happens to be aligned coplanar with the Y-Z plane (coming out of the page) as seen in FIG.  16 . Removing facet material or cutting tip stock material with a grinding wheel or other rotational machining tool when forming a portion of a facet such as when grinding wheel  806  is forming a bevel  500 , is in essence cutting or making a cut from the cutting tip stock material when fabricating it as according to this invention. 
     FIG. 18 shows a grinding wheel  812  which has a radius of rotation  816 , an axial thickness  814  and an exterior circumferential profile  840 . FIG. 19 shows a grinding wheel  818  which has a radius of rotation  822 , an axial thickness  820  and an exterior circumferential profile  842 . Both grinding wheels  812  and  818  could be used to grind bevels similar to bevels  500 - 500 - 500  upon facets  400 - 400 - 400  of cutting tip  200 , however due to their different exterior circumferential profiles and potentially different axial thicknesses, potentially different radii of rotation and the different possible relations their axises of rotation can be oriented with respect to the three dimensions of the X-Y-Z axises of corresponding cutting tips, the bevels grinding wheels  812  and  818  would grind could have a variety of different shapes, slopes and/or curvatures than that of bevels  500 - 500 - 500  as shown on cutting tip  200 . 
     FIGS. 20-25 illustrate in part another method of manufacturing a cutting tip  206  that is similar to cutting tip  200  and similar to the method as disclosed in FIGS. 12-17 except the method of manufacturing cutting tip  206  as illustrated in FIGS. 20-25 first entails grinding the hollow ground trocar tip facets  402 - 402 - 402  by a grinding wheel  824  as illustrated in FIG. 22 wherein the axis of rotation  1014  of grinding wheel  824  is oriented substantially perpendicular to central longitudinal axis  1018  of cutting tip  206  when grinding each facet  402  thereon. Grinding wheel  824  has a radius of rotation  828 , an axial thickness  826 , and an exterior circumferential profile  844 . Axis of rotation  1014  of grinding wheel  824  is oriented in a specific spatial orientation when grinding a hollow ground facet  402  on cutting tip  206 , particularly axis of rotation  1014  is spatially oriented substantially perpendicular to both a central longitudinal axis  1018  or the Y-axis and to the Z-axis, while being substantially parallel to the X-axis. Axis of rotation  1014  of grinding wheel  824 , when grinding wheel  824  is grinding each facet  402  upon cutting tip  206 , is therefore not inclined relative to any of the X-Y-Z axises nor any of the three dimensions. FIGS. 24 &amp; 25 show that another grinding wheel  830  next grinds a bevel  502  upon each of the facets  402  after grinding wheel  824  formed facets  402 - 402 - 402 . Bevels  502 - 502 - 502  create a sharper cutting edge  302  at the facet junctures of cutting tip  206  than is attainable by a conventional trocar tip having only hollow ground facets as shown for example in FIGS. 20 &amp; 21, while allowing cutting tip  206  to retain sufficient structural facet strength to crush/split heavy bone and easily push penetrated material from its cutting path. Each bevel  502  creates a bevel boundary  602  upon its corresponding facet  402 . Grinding wheel  830  has a radius of rotation  834 , an axial thickness  832  and an exterior circumferential profile  846 . The radius of rotation  834  of grinding wheel  830  is of a different length of radius than the radius of rotation  828  of grinding wheel  824 . The axial thickness  832  of grinding wheel  830  is of a different thickness than the axial thickness  826  of grinding wheel  824 . The exterior circumferential profile  846  of grinding wheel  830  is also of a different profile than the exterior circumferential profile  844  of grinding wheel  824 . 
     As is illustrated in FIGS. 24 &amp; 25 axis of rotation  1016  of grinding wheel  830  is inclined relative to each of the X, and Z axises in a specific spatial orientation and therefore to two of the corresponding three dimensional planes -the X-Y, and Y-Z planes- when grinding wheel  830  is forming each bevel  502  thereon. However, axis of rotation  1016  of grinding wheel  830  is perpendicular to the Y-axis or central longitudinal axis  1018  of cutting tip  206  and is parallel to the X-Z plane when grinding wheel  830  is forming each bevel  502 . Therefore, the axis of rotation  1016  of grinding wheel  830  when forming a bevel  502  upon a particular facet  402  of cutting tip  206  is oriented with respect to at least one of the X-Y-Z axises and corresponding three dimensional planes in a different relation or spatial orientation than the spatial orientation axis of rotation  1014  of grinding wheel  824  is oriented with respect to the X-Y-Z axises and three dimensional planes when forming the particular facet. Each bevel  502  is substantially on only one bisected side of its corresponding facet  402 , thus grinding wheel  830  when forming a bevel  502  upon a facet  402  is removing facet material or cutting tip stock material from only one bisected side of facet  402  for a substantial majority of the time that grinding wheel  830  is forming the particular bevel  502 . This is clearly illustrated in FIG. 24 where the bevel  502  grinding wheel  830  is shown forming is substantially completely on the right side of facet bisecting plane  660 , which bisecting plane  660  happens to be aligned coplanar with the Y-Z plane (coming out of the page) as seen in FIG.  24 . 
     It is apparent that the facets of the cutting tips as according to this invention whether concave/hollow ground or of some other shape may have each primary facet structure such as hollow ground facets  402 - 402 - 402  of the conventional trocar tip as illustrated in FIGS. 20 &amp; 21, formed by rotational machining tools and/or grinding wheels where the axis of rotation of the rotational machining tool or grinding wheel forming such primary facet structure is substantially inclined relative to one or more of the Cartesian X-Y-Z axises and their corresponding three dimensional planes as has been disclosed in this specification, when forming the corresponding portion of each facet. The term primary facet structure refers generally but not limited thereto, to the facet before a bevel or bevels as according to this invention are formed or ground thereon so as to create a razor sharp cutting edge as is according to the desired results of this invention. Such cutting tips having the primary facet structures or at least a part of a facet formed by a grinding wheel or rotational machining tool whose axis of rotation is inclined with respect to at least one or more of the X-Y-Z axises would then have a bevel or bevels as according to this invention formed on each facet by a grinding wheel or rotational machining tool which would have possibly a different radius of rotation, a different axial thickness, or a different exterior circumferential profile than the grinding wheel or rotational machining tool that formed the primary facet structure. Also, the grinding wheel or rotational machining tool forming the bevel or bevels on the primary facet structure could possibly have its axis of rotation when forming the bevel(s) on a facet of a respective cutting tip, oriented with respect to the X-Y-Z axises in a different manner or relation than the inclined manner or relation the grinding wheel or rotational machining tool that formed the primary facet structure of that facet was oriented with respect to the X-Y-Z axises when forming the primary facet structure as according to this invention. Such different manner or relation of orientation of the axis of rotation of the rotational machining tool or grinding wheel when forming the bevel(s) with respect to the X-Y-Z axises could be either inclined or non-inclined relative to one or more of the X-Y-Z axises and the corresponding three dimensional planes. 
     FIGS. 26-35 illustrate other preferred cutting tip embodiments as according to the cutting tips of this invention that have at least a part of their facets substantially concave—which may have been formed from hollow grinding and/or other fabrication methods. FIGS. 26 &amp; 27 show cross-sectional views of a three sided cutting tip  208  having facets  404 - 404 - 404 , cutting edges  304 - 304 - 304 , bevels  504 - 504 - 504 , and bevel boundaries  604 - 604 - 604 . FIGS. 28 &amp; 29 show cross-sectional views of a three sided cutting tip  210  having facets  406 - 406 - 406 , cutting edges  306 - 306 - 306 , bevels  506 - 506 - 506 , and bevel boundaries  606 - 606 - 606 . FIGS. 30 &amp; 31 show cross-sectional views of a three sided cutting tip  212  having facets  408 - 408 - 408 , cutting edges  308 - 308 - 308 , bevels  508 - 508 - 508 , and bevel boundaries  608 - 608 - 608 . FIGS. 32 &amp; 33 show cross-sectional views of a three sided cutting tip  214  having facets  410 - 410 - 410 , cutting edges  310 - 310 - 310 , bevels  510 - 510 - 510 , and bevel boundaries  610 - 610 - 610 . FIGS. 34 &amp; 35 show cross-sectional views of a three sided cutting tip  216  having facets  412 - 412 - 412 , cutting edges  312 - 312 - 312 , bevels  512 - 512 - 512 , and bevel boundaries  612 - 612 - 612 . 
     As is apparent from cutting tips  210  &amp;  212  as illustrated in FIGS. 28-31 regardless of how small the distal angle is or how dished-out the concave facets are, a finer or narrower proximal angle is attainable at the cutting edge or juncture of adjoining facets by forming a bevel thereon as according to this invention, and therefore provides a sharper cutting edge than would of been attainable had the bevel or bevels not been formed. 
     FIGS. 36-40 illustrate a cutting tip  218 . Cutting tip  218  has facets  414 - 414 - 414 , cutting edges  314 - 314 - 314 , bevels  514 - 514 - 514 , and bevel boundaries  614 - 614 - 614 . Cutting tip  218  is similar to the cutting tips described above except that the facets  414 - 414 - 414  of cutting tip  218  are substantially flat as is best seen in FIG.  39 . FIG. 40 shows that a proximal angle  674  has an angle of measure that is less than the angle of measure of a distal angle  676  as according to the proximal and distal angles of this invention and therefore gives cutting tip  218  sharper cutting edges  314 - 314 - 314  than it would of had if the bevels  514 - 514 - 514  had not been formed thereon. It is apparent that other proximal angles having an angle of measure that is greater than the angle of measure of proximal angle  674  are measurable by reference from other locations along bevel  514  of cutting tip  218 . Such other proximal angles would still have an angle of measure that is less than the angle of measure of distal angle  676  as is according to this invention. 
     It is apparent that the shape or structure of the facets according to the cutting tips of this invention may be concave, flat, convex or have other complex geometries as according to the scope of this invention. 
     FIGS. 41-45 illustrate a cutting tip  220 . Cutting tip  220  has facets  416 - 416 - 416 , cutting edges  316 - 316 - 316 , bevels  516 - 516 - 516 - 516 - 516 - 516 , and bevel boundaries  616 - 616 - 616 - 616 - 616 - 616 . Cutting tip  220  has two bevels  516 - 516  formed upon each facet  416 . It is apparent that more than one bevel may be formed upon each facet of the cutting tips as according to this invention. FIG. 45 shows that a proximal angle  678  has an angle of measure that is less than the angle of measure of a distal angle  680  as according to the proximal and distal angles of this invention and therefore gives cutting tip  220  sharper cutting edges  316 - 316 - 316  than it would of had if the bevels had not been formed thereon. 
     FIGS. 46-49 illustrate other arrowheads and surgical trocars having cutting tips as according to this invention at their leading penetrating ends. FIG. 46 illustrates a fixed-blade arrowhead  752  that has cutting blades  722 - 722 - 722  and cutting tip  220  removably attached to arrowhead body  732 . FIG. 47 illustrates a blade-opening arrowhead  750  that has pivotal cutting blades  720 - 720 - 720  and cutting tip  222  integrally attached to or with arrowhead body  731 . FIG. 48 illustrates a surgical trocar  754  that has a cannula  740  or trocar tube, a mandrel shank  744  or trocar obturator shank with cutting tip  220  removably attached thereto. FIG. 49 illustrates another surgical trocar  756  similar to surgical trocar  754  except for a cutting tip  224  is integrally attached with a mandrel shank  742 . 
     FIGS. 50-53 illustrate other examples of cutting tips as according to this invention that have two bevels upon each facet such that one bevel of each adjoining facet communicates with each cutting edge. FIGS. 50-51 illustrate a cutting tip  226 . Cutting tip  226  has flat facets  418 - 418 - 418 , cutting edges  318 - 318 - 318 , bevels  518 - 518 - 518 - 518 - 518 - 518 , and bevel boundaries  618 - 618 - 618 - 618 - 618 - 618 . FIGS. 52-53 illustrate a cutting tip  228 . Cutting tip  228  also has flat facets  420 - 420 - 420 , cutting edges  320 - 320 - 320 , bevels  520 - 520 - 520 - 520 - 520 - 520 , and bevel boundaries  620 - 620 - 620 - 620 - 620 - 620 . 
     It is apparent that cutting tips as according to this invention could have facets that have only one bevel formed thereon while having other facets that have a plurality of bevels formed thereon. 
     FIGS. 54-56 illustrate a cutting tip  230 . Cutting tip  230  has hollow ground facets  422 - 422 - 422 , cutting edges  322 - 322 - 322 , bevels  526 - 526 - 526 , hone bevels  528 - 528 - 528 , and bevel boundaries  622 - 622 - 622 . Hone bevels  528 - 528 - 528  serve to provide cutting tip  230  and other cutting tips as according to this invention that have hone bevels or their equivalents with a slightly stronger cutting edge as is commonly done with razor blades, scalpels and other cutting knife type blades, which are generally fabricated from the process of strip grinding. As illustrated in FIG. 56 a proximal angle  690  has an angle of measure that is less than a distal angle  692  as according to this invention. The dotted lines  1032  &amp;  1036  of angle  692  do not intersect each other at cutting edge  322  nor do the dotted lines  1036  &amp;  1034  of angle  690  intersect each other at cutting edge  322 . This is an example as according to this invention of how the method of determining the angle or angles that adjoining facets, bevels, other cutting tip structures or their equivalents are offset from each other with respect to the shape of their corresponding cutting tips and cutting edges as according to this invention, may not involve referencing from the corresponding cutting edge, but which still determine true angular offsets of such structures. 
     It is apparent that a proximal angle of less degrees in measure than a distal angle as according to this invention is attainable with cutting tip  230  and other similar preferred cutting tip embodiments of this invention having hone bevels despite the fact that each hone bevel, as for example hone bevels  528 - 528 - 528  of cutting tip  230 , creates a wider angle than the corresponding proximal angle of the cutting tip in reference at a location closer to the corresponding cutting edge than the structure of the cutting tip that was used in reference to determine the angle of measure of the comparative proximal angle. Such a wider angle, or wider angles therefore could be determined as according to one measuring method by angular measuring reference points that are closer to corresponding cutting edges than the angular measuring reference points of the corresponding comparative proximal angle or proximal angles of the cutting tip and cutting edge in reference as has been defined in this specification. 
     FIGS. 57 &amp; 58 illustrate a cutting tip  234  and a cutting tip  236 . Cutting tips  234  &amp;  236  are identical to each other in certain structural features such as they each have facets  426 - 426 - 426 , bevels  530 - 530 - 530 , and bevel boundaries  626 - 626 - 626 . Cutting tips  234  &amp;  236  however differ from each other in the location of their hone bevels and therefore the location of their cutting edges. Each hone bevel  532  of cutting tip  234  is located on the left side of its accompanying cutting edge  326  as seen when viewed from above in cross-section as depicted in FIG. 58, whereas each hone bevel  534  of cutting tip  236  is located on the right side of its accompanying cutting edge  328  as seen when viewed from above in cross-section as depicted in FIG.  57 . 
     The bevel boundaries of the cutting tips as according to this invention generally define a location or boundary upon respective cutting tips where the structure of the cutting tip, particularly facets or area between cutting edges, change slope or change shape. Such change in slope or shape is generally best seen from cross-sectional views of the cutting tips but is also readily apparent from side views and top views of the respective cutting tips. It is apparent that the cutting tips as according to this invention having hone bevels or equivalents may also have hone bevel boundaries. 
     FIGS. 59 &amp; 60 illustrate a cutting tip  232 . Cutting tip  232  has facets  424 - 424 - 424 , cutting edges  324 - 324 - 324 , bevels  522 - 522 - 522 - 522 - 522 - 522 , hone bevels  524 - 524 - 524 - 524 - 524 - 524  and bevel boundaries  624 - 624 - 624 - 624 - 624 - 624 . As is clearly evident from the enlarged view of one of the cutting edges  324  of cutting tip  232  as illustrated in FIG. 60, each cutting edge  324  has two hone bevels  524 - 524  situated on opposite sides thereof. 
     FIGS. 61-64 illustrate a cutting tip  238 , yet another preferred embodiment as according to this invention. Cutting tip  238  has concave facets  430 - 430 - 430 , cutting edges  330 - 330 - 330 , flat planar bevels  536 - 536 - 536 - 536 - 536 - 536 , and bevel boundaries  630 - 630 - 630 - 630 - 630 - 630 . FIG. 64 illustrates that a proximal angle  686  has an angle of measure that is less than the angle of measure of a distal angle  688  as according to the proximal and distal angles of this invention and also that a proximal angle  682  has an angle of measure that is less than the angle of measure of a distal angle  684 . Angles  682  &amp;  684  of FIG. 64 illustrate another example showing that the manner of determining the angle of measure of a particular structure or section of a cutting tip as according to this invention is not limited exclusively to angular measuring reference points and distances they are displaced from their corresponding cutting edges. For example, even though dotted lines  1020  &amp;  1022  of angle  684  intersect adjoining facets  430 - 430  at facet bisecting planes  660 - 660  and do not conjoin at a cutting edge  330  but rather at a point  1030  along one of the facet bisecting planes  660 , which coincidently bisects angle  684  into two substantially equal halves, they accurately represent an angle that adjoining facets  430 - 430  are offset from each other with respect to the shape of a section of cutting tip  238  that is distal or further from the cutting edge than the corresponding bevel boundaries  630 - 630 . 
     The term distal as used throughout this specification refers to being further away from whereas the term proximal refers to being closer to. Distal and proximal have been referenced from corresponding cutting edges with respect to proximal and distal angles, so therefore distal angles are determined from the angular offset of opposing cutting tip structures, such a facets and bevels, that are located a distance further from the cutting edge than opposing cutting tip structures that determine the angular offset of proximal angles, regardless of the cutting tip geometry, as has been discussed herein. 
     It is apparent that there exists a variety of angle measuring methods, some of which have been discussed herein, to determine that a particular section of a cutting tip, as according to this invention, which is located substantially closer to a corresponding cutting edge has a finer or narrower angle than a section of the same cutting tip located a distance substantially further from the same corresponding cutting edge, which generally but not limited to is determined as in a plane perpendicular to the central longitudinal axis of the respective cutting tip. Such cutting tips as according to the desired results of the cutting tips of this invention overcome deficiencies inherent in prior art cutting tips by providing a razor sharp cutting edge in combination with optimally desirable strong and durable facet structure. 
     FIG. 65 illustrates a cutting tip  240 . Cutting tip  240  has convex facets  432 - 432 - 432 , cutting edges  332 - 332 - 332 , flat planar bevels  538 - 538 - 538 - 538 - 538 - 538 , and bevel boundaries  632 - 632 - 632 - 632 - 632 - 632 . Cutting tip  240  is similar to cutting tip  238  as illustrated in FIGS. 61-64, except cutting tip  240  has convex or outwardly bulging facets, and therefore is a generally conical shaped cutting tip. 
     Although the cutting tips as according to this invention that are fabricated by machining—i.e. screw machines, grinding etc.—are preferably fabricated from round bar or rod stock, such as 12 foot lengths of stainless steel bar, it is apparent that a step in the manufacturing process to produce cutting tips as according to this invention could involve impact swaging of pellets or slugs to form at least part of the primary shape or structure of a cutting tip, wherein after the razor sharp cutting edges and/or bevels could be ground thereon after hardening was completed. Impact swaging could allow cutting tips, as according to some of the preferred embodiments of this invention which have facet structures that are complex and costly to machine such as the convex facets  432 - 432 - 432  of cutting tip  240 , to be economically and quickly produced. 
     It is apparent that flat bevels such as bevels  538  of cutting tip  240  as illustrated in FIG. 65 could be swaged or formed during impact swaging and that hone bevels or other bevels, such as curved bevels could then be ground or formed thereon to provide a sharper cutting edge as according to the desired results of this invention. 
     FIGS. 66-68 illustrate a cutting tip  242 . Cutting tip  242  differs from the other cutting tips of this invention that have been heretofore disclosed in that cutting tip  242  has attachable tip blades  350 - 350 - 350 , which each fit into a corresponding slot  910  of a metal tip body  1040  as is illustrated in FIG.  68 . Tip blades  350 - 350 - 350  each have a pair of bevels  540 - 540  and a cutting edge  334 . Each tip blade  350  abuts against a nipple  908  of tip body  1040  and against a pair of bevel boundaries  628 - 628  when attached thereto. Nipple  908  is preferably integral with tip body  1040 . Tip blades  350 - 350 - 350  are preferably welded integrally to tip body  1040 . It is apparent that tip blades  350 - 350 - 350  and other tip blades or their equivalents as according to this invention may be attached to tip bodies, whether of metal construction, polymer or of other materials or combinations thereof, by a variety of different methods including glueing, welding, molding, and by modifications in the shapes of the tip blades and/or tip bodies. 
     FIGS. 69-72 illustrate a cutting tip  244 . Cutting tip  244  differs from the other cutting tips of this invention that have been heretofore disclosed in that cutting tip  244  has three integral cutting edges  336 - 336 - 336  that each extend substantially the full length of cutting tip  244  from the junctures between the facets rearward along a barrel section  906 . A pair of bevel boundaries  634   a - 634   a  defines the boundary of a corresponding pair of bevels  542 - 542  with corresponding facets, as is illustrated in FIG.  71 . Another pair of bevel boundaries  634   b - 634   b  defines the boundary of a pair of corresponding bevels  544 - 544  with barrel section  906 , as is illustrated in FIG.  72 . Cutting edge  336  between each pair of adjoining facets is coplanar or in-line with the section of cutting edge  336  that extends rearward upon barrel section  906 . 
     FIGS. 73-76 illustrate a cutting tip  246 . Cutting tip  246  is similar to cutting tip  244  as illustrated in FIGS. 69-72 except for the three cutting edges  338 - 338 - 338  of cutting tip  246  are the razor edges of attachable tip blades  352 - 352 - 352 , which each fit into a corresponding slot  912  of a metal tip body  1042  as is illustrated in FIG.  76 . Tip blades  352 - 352 - 352  each have a pair of bevels  546 - 546  that are situated between adjacent facets and form bevel boundaries  636   a - 636   a  thereat. Each tip blade  352  also has a pair of bevels  548 - 548  that run along barrel section  907  and form bevel boundaries  636   b - 636   b  thereat. 
     FIGS. 77-81 illustrate cutting tips  248 ,  250 ,  252  &amp;  254  which all in common have bevels on both sides of their facet junctures such that the bevels do not extend completely to the forward leading apex of their respective cutting tips. Cutting tip  248  as illustrated in FIGS. 77 &amp; 78 has three facets  434 - 434 - 434 , a pair of bevels  550 - 550  that forms each cutting edge  340  and a three sided apex  917 . It is apparent that each side of apex  917  could be hollow ground and therefore substantially concave. Each facet has a curved section  552  between bevels  550 - 550  thereon. It is apparent that the facets of cutting tip  248  could be cut or formed at least in part from a rotational machining tool whose axis of rotation changes in spatial orientation relative to the X-Y-Z axises of cutting tip  248  while forming a complete cut or at least a portion thereof. Cutting tip  248  has a barrel section  914  that is necked down as illustrated in FIG.  77 . Cutting tip  250  as illustrated in FIG. 79 has four facets each with a cutting edge  342  that extends from between facet junctures rewards upon barrel section  914  thereof. Cutting tip  252  as illustrated in FIG. 80 is similar to cutting tip  250  except the four cutting edges  344 - 344 - 344 - 344  of cutting tip  252  are found only along the junctures between the respective facets. Cutting tip  254  as illustrated in FIG. 81 has a substantially blunt apex  916 , and four flat planar facets each with a cutting edge  346  that is found only along the junctures between the respective facets. 
     It is apparent that the cutting tips of this invention may have cutting edges as according to this invention along any axial length of their structure, whether integrally formed with, integrally attached or removably attachable to their respective cutting tips. It is also apparent that the cutting edges of a cutting tip as according to this invention may be aligned or oriented with respect to the central longitudinal axis thereof, the three dimensions as depicted in this specification by a Cartesian X-Y-Z axis system wherein the Y-axis is collinear with the central longitudinal axis thereof, and the facet junctures of their respective cutting tip in a variety of different manners. Such different aligned or oriented manners of the cutting edges include being inclined relative to one or more of the X, Y or Z axises and not being coplanar with a corresponding facet juncture. It is also apparent that cutting edges as according to this invention that are situated upon the barrel sections or equivalents of their respective cutting tips may be aligned or oriented with respect to the facet junctures of their cutting tips in a variety of manners, including not being in-line or coplanar with them. 
     FIGS. 82-84 illustrate a cutting tip  256 . Cutting tip  256  has attachable tip blades  354 - 354 - 354  each having a cutting edge  348  and a pair of bevels  554 - 554 . Each tip blade  354  fits into a slot  920  in the barrel section  918  of tip body  1044  where a pair of bevel boundaries  640 - 640  contact each tip blade  354 . Tip body  1044  is preferably of a metal construction and tip blades  354 - 354 - 354  are preferably non-removably attached to tip body  1044  by welding, such as capillary welding or other welding techniques, but not limited thereto. 
     FIG. 85 illustrates a blade-opening arrowhead  758  with cutting tip  256  attached at the leading penetrating end. 
     FIGS. 86 &amp; 87 illustrate a cutting tip  258  similar to cutting tip  256 , but which is integrally attached with an arrowhead body  734  of a blade-opening arrowhead  760 . 
     FIG. 88 illustrates a cross-section of a cutting tip  259  which is similar to cutting tip  258  of blade-opening arrowhead  734 , except the tip blades are integrally fabricated with cutting tip  259 . 
     Securement means as according to this invention has the intended meaning that a removably attachable tip blade or equivalent is retained in a cutting position when assembled with or to a corresponding tip body such that a plane perpendicular to the central longitudinal axis of the cutting tip intersects both a holding element, and a portion of the tip blade that is situated closer to the central longitudinal axis of the cutting tip than the holding element. Holding elements as according to this invention comprise portions of tip bodies, arrowhead bodies or mandrels, arrowhead blades, or other suitable structure or structures of the penetrating device utilizing such a cutting tip as according to this invention, or any combination of such structures that serve to limit undesired displacement or movement of tip blades. In this manner the tip blades will engage against the holding element or elements and therefore resist displacement in a radial direction as well as in axial directions from the tip body, thus securing the tip blades to their respective cutting tips. 
     FIGS. 89 &amp; 90 illustrate an example of securement means as according to this invention where a cutting tip  260  is shown to be removably attachable to a blade-opening arrowhead body. Cutting tip  260  has three facets, three slots  928 - 928 - 928  each with a catch-lip  926 , three removably attachable tip blades  356 - 356 - 356  (only two tip blades  356 - 356  are shown for reasons of simplicity and illustration), and a tip body  1046  having an internally threaded female cavity  930  that threads onto a threaded male stud  762  of the arrowhead body. Each tip blade  356  has a notch  932  and a protrusion  933 . Therefore, when tip blades  356 - 356 - 356  are inserted into slots  928 - 928 - 928  and tip body  1046  is threaded onto stud  762  each notch  932  mates with each corresponding catch-lip  926  such that each protrusion  933  is positioned forward of the rearward terminus of its corresponding catch-lip  926  thereby securing each tip blade  356  to tip body  1046  as according to the securement means of this invention. As is clearly illustrated in FIG. 90 a plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  260  intersects protrusion  933  of each tip blade at a location closer to the central longitudinal axis of cutting tip  260  than the locations plane  1028  intersects each corresponding catch-lip  926  of tip body  1046 , as is according to the securement means of this invention. Catch-lips  926 - 926 - 926  are examples of holding elements as according to the securement means of this invention. 
     FIG. 91 illustrates a tip blade  360  which is similar to tip blade  356  except tip blade  360  has a sloped rear edge  934  which will minimize any possible barbing effect that could occur when a corresponding cutting tip is retracted from the substance it had penetrated. 
     FIGS. 92 &amp; 93 illustrate another example of securement means as according to this invention where a cutting tip  264  is shown to be removably attachable to a blade-opening arrowhead body. Cutting tip  264  has three facets, three slots  928 - 928 - 928  each with a catch-lip  926 , three removably attachable tip blades  362 - 362 - 362 , and a tip body  1046  having an internally threaded female cavity  930  that threads onto a threaded male stud  782  of the arrowhead body. Stud  782  has a depression  764  centrally axially formed at its forward end, as is illustrated in FIG.  92 . Each tip blade  362  has a prong  940  and an arm  938 . Prongs  940 - 940 - 940  are similar to protrusion  933 - 933 - 933  except that each prong  940  extends in a rearward direction when tip blades  362 - 362 - 362  are secured to cutting tip  264 , whereas each protrusion  933  extends in a forward direction when tip blades  356 - 356 - 356  are secured to cutting tip  260 . Therefore, when tip blades  362 - 362 - 362  are inserted into slots  928 - 928 - 928  and tip body  1046  is threaded onto stud  782  each prong  940  mates within depression  764  such that each prong  940  is positioned rearward of the forward terminus of stud  782  thereby securing each tip blade  362  to tip body  1046  as according to the securement means of this invention. As is clearly illustrated in FIG. 93 plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  264  intersects each prong  940  of each tip blade at a location closer to the central longitudinal axis of cutting tip  264  than the locations plane  1028  intersects stud  782  of tip body  1046 , as is according to the securement means of this invention. It is apparent that tip blades  362 - 362 - 362  could also each have a protrusion  933  and a notch  932  so as to mate with catch-lips  926  to further aid in the securement of tip blades to tip body  1046 , as according to the desired results of this invention. 
     FIGS. 94-96 illustrate another example of securement means as according to this invention where a cutting tip  266  is shown to be removably attachable to a blade-opening arrowhead body. Cutting tip  266  has three facets, three slots  986 - 986 - 986  each with a catch-lip  926 , three removably attachable tip blades  364 - 364 - 364 , and a tip body  1048  having an internally threaded female cavity  944  that threads onto a threaded male stud  784  of the arrowhead body. Internal cavity  944  has a larger diameter flange cavity  946  situated rearward of the threaded internal section as is illustrated in FIG.  94 . Each tip blade  364  has a flange  942  as is illustrated in FIG.  96 . Each flange  942  is substantially not coplanar with at least another section of its corresponding tip blade  364  as is clearly illustrated in FIG.  96 . Therefore, when tip blades  364 - 364 - 364  are inserted into slots  986 - 986 - 986  and tip body  1048  is threaded onto stud  784  each flange  942  mates within flange cavity  946  such that each flange  942  is positioned circumferentially or laterally away from the opening of its corresponding slot  986  and against the inside wall of flange cavity  946  thereby securing each tip blade  364  to tip body  1048  as according to the securement means of this invention. As is clearly illustrated in FIG. 95 a plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  266  intersects each flange  942  of each tip blade at a location closer to the central longitudinal axis of cutting tip  266  than the locations plane  1028  intersects tip body  1048 , as is according to the securement means of this invention. 
     As is illustrated in FIGS. 97 a-c  it is apparent that tip blades having flanges  942  in combination with other tip blade structures as disclosed herein will further aid in the securement of the tips blades to corresponding tip bodies, as according to the securement means of this invention. 
     FIGS. 98 &amp; 99 illustrate another example of securement means as according to this invention where a cutting tip  268  is shown to be removably attachable to a blade-opening arrowhead body. Cutting tip  268  has three facets, three slots  986 - 986 - 986  each with a catch-lip  926 , three removably attachable tip blades (of which one is a tip blade  366  and another is a tip blade  368 ) as is illustrated in FIG. 98, and a tip body  1048  having an internally threaded female cavity that threads onto stud  784  of the arrowhead body. For reasons of simplicity FIGS. 98 &amp; 99 show only two tip blades  366  and  368 , but it is apparent that cutting tip  268  utilizes three tip blades. The arrowhead body has an annular recess  768  situated about stud  784 . Tip blade  366  has a leg  952  and tip blade  368  has a leg  954 . Leg  954  of tip blade  368  is an extension of flange  942 . Therefore, when both blades  366  &amp;  368  are inserted into their slots  986 - 986  and tip body  1048  is threaded onto stud  784  leg  954  of tip blade  368  and leg  952  of tip blade  366  mate within annular recess  768  such that each leg is positioned rearward of the forward terminus of annular recess  768  thereby securing each tip blade  366  &amp;  368  to tip body  1048  as according to the securement means of this invention. As is clearly illustrated in FIG. 99 plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  268  intersects leg  954  of tip blade  368  and leg  952  of tip blade  366  at locations closer to the central longitudinal axis of cutting tip  268  than the locations plane  1028  intersects the arrowhead body, as is according to the securement means of this invention. As is obvious from FIG. 99 tip blades  366  &amp;  368  may also incorporate other structural tip blade variations of the securement means according to this invention as have been disclosed herein, in combination with legs  952  &amp;  954  or their equivalents which mate in annular recesses like annular recess  768 . 
     FIGS. 100 &amp; 101 illustrate yet another example of securement means as according to this invention where a cutting tip  270  is shown to be removably attachable to a blade-opening arrowhead body. Cutting tip  270  has three facets, three slots  960 - 960 - 960 , three removably attachable tip blades  370 - 370 - 370 , and a tip body  1050 . Tip body  1050  has an undercut cavity  958 , a sloped undercut wall  970 , an externally threaded male stud  962  that threads into a threaded female cavity  968  of the arrowhead body. Sloped undercut wall  970  abuts against an annular shelf  966  of the arrowhead body when tip body  1050  is attached thereto. The arrowhead body has a larger diameter leg cavity  984  situated forward of threaded internal cavity  968  as is illustrated in FIG.  100 . Each tip blade  370  has an abutment edge  972  which abuts against annular shelf  966  of the arrowhead body as is illustrated in FIG.  101 . Each tip blade  370  has a leg  956  so that when tip blades  370 - 370 - 370  are inserted into slots  960 - 960 - 960  and tip body  1050  is threaded into cavity  968  each leg  956  mates within leg cavity  984  such that at least a portion of each leg  956  is positioned rearward of the forward terminus of the arrowhead body and against the inside wall of leg cavity  984  thereby securing each tip blade  370  to tip body  1050  as according to the securement means of this invention. As is clearly illustrated in FIG. 101 plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  270  intersects each leg  956  of each tip blade  370  at a location closer to the central longitudinal axis of cutting tip  270  than the locations plane  1028  intersects the arrowhead body, as according to the securement means of this invention. 
     FIG. 102 illustrates a tip blade  372  having a notch  927  and a protrusion  935 . Tip blade  372  shows that catch-lip, notch and protrusion type securing features can be combined with legs  956  or their equivalents of the tip blades of this invention similar to a tip blade  370  so as to enhance the securement of the tip blades to their tip bodies. 
     FIGS. 103-106 illustrate how an example of securement means similar to the securement means embodiment as illustrated in FIGS. 100-101 as according to this invention is applicable to a fixed-blade arrowhead. FIG. 105 shows that a cutting tip  271  is removably attachable to a fixed-blade arrowhead body. Each forward edge section  774  of the fixed cutting blades of the arrowhead abut against corresponding abutment edges  972 - 972 - 972  of tip blades  372 - 372 - 372  when the arrowhead is assembled as is illustrated in FIG.  104 . Tip body  1051  differs from tip body  1050  of cutting tip  270  as illustrated in FIGS. 100 &amp; 101 in that tip body  1051  has a void  929  and a catch-lip  937  in each slot  966  thereof. Each tip blade  372  has a protrusion  935  and a notch  927 . Therefore, when tip blades  372 - 372 - 372  are inserted into slots  966 - 966 - 966  and tip body  1051  is threaded into the arrowhead body, each notch  927  mates with each corresponding catch-lip  937  such that each protrusion  935  is positioned forward of the rearward terminus of its corresponding catch-lip  937  thereby securing each tip blade  372  to tip body  1051  as according to the securement means of this invention. As is clearly illustrated in FIG. 104 plane  1028  which is perpendicular to the central longitudinal axis of cutting tip  271  intersects protrusion  935  of each tip blade at a location closer to the central longitudinal axis of cutting tip  271  than the locations plane  1028  intersects each corresponding catch-lip  937  of tip body  1051 , as is according to the securement means of this invention. 
     It is apparent that the securement means as according to this invention may be used to secure tip blades or their equivalents between facet junctures of cutting tips as according to this invention. 
     FIG. 107 illustrates a forward end  772  of a fixed-blade arrowhead blade  726 . It is apparent that the forward end of the fixed-blade arrowhead blades used in conjunction with cutting tips of this invention having tip blades, may have different shapes such as being substantially flat, so as to optimally fit with their corresponding cutting tip. 
     FIGS. 108 &amp; 109 illustrate a cutting tip  272  of a fixed-blade arrowhead, which has fixed-blade arrowhead cutting blades  728 - 728 - 728 . Each cutting blade  728  has a substantially straight cutting edge  982  at its forward end that abuts against an abutment edge  976  of a tip blade  376  which is secured to a female screw on type tip body  1052  as according to the securement means of this invention. Cutting tip  272  as illustrated in FIG. 109 provides razor sharp tip blades or cutting blades on a chisel type cutting tip while also allowing to lock the upper section  982  of a fixed cutting blade  728  to an arrowhead body by tucking the forward end of the arrowhead blade in an undercut cavity of the chisel type tip—as is a very common practice in the archery industry. 
     FIG. 111 shows a press-on fit tip  274  which has tip blades  378 - 378 - 378 , an undercut wall  980  that abuts against an annular shelf  780  of the arrowhead body, and an internal female cavity  978  which fits around a male stud  778  of the arrowhead body when tip  274  is pressed thereon. 
     It is apparent that there are many methods of attaching the cutting tips as according to this invention to their respective penetrating devices, including forming them integrally thereon. 
     FIGS. 112 &amp; 113 illustrated a press-on fit cutting tip  276 . Cutting tip  276  is similar to cutting tip  274  as illustrated in FIG. 111 except cutting tip  276  has cutting edges  330 - 330 - 330  and accompanying bevels as according to this invention located at the facet junctures in addition to having tip blades  378 - 378 - 378  on the barrel section thereof. 
     It is apparent that the cutting tips as according to this invention may have both true cutting edges or razor sharp cutting edges as according to this invention at their facet junctures or equivalents as well as on their barrel sections or equivalents, which may comprise tip blades as have been disclosed herein. It is apparent that any of the different facet juncture cutting edge designs as illustrated or suggested herein may be combined with any of the tip blade designs, including in manners that have not been suggested herein. 
     It is apparent that different cutting tips as according to the desired results of this invention exist which have not been discussed above. It is apparent that the different parts and structural shapes and their equivalents as according to the cutting tips of this invention, as discussed above and as according to other preferred embodiments of this invention, can be changed, or interchanged, or eliminated, or duplicated, or made of different materials, and connected to or associated with adjacent elements in different manners, other than suggested herein, without deterring from the desired results of the cutting tips as according to this invention. 
     For example FIGS. 114 &amp; 115 show a cutting tip  278  that has both integral cutting edges  316 - 316 - 316  each formed by a pair of bevels  516 - 516  at facet junctures, in conjunction with cutting edges  376 - 376 - 376  of tip blades  378 - 378 - 378  on the barrel section thereof. 
     Also FIGS. 116 &amp; 117 illustrate a cutting tip  280  that has both integral cutting edges  300 - 300 - 300  each formed by a corresponding bevel  500  at facet junctures, and cutting edges  376 - 376 - 376  of tip blades  378 - 378 - 378  on the barrel section thereof. It is apparent that cutting edges  376 - 376 - 376  could be integrally formed with the barrel section of cutting tip  280  or that they could be attachable whether removably so or not. It is apparent that each cutting edge  376  may be an integrally ground part of the barrel section of cutting tip  280 . 
     FIGS. 118-131 illustrate cross-sectional views of cutting tips  282 - 294  as according to this invention. Cutting tips  282 - 294  illustrate other possible structural arrangements of facet sections and/or barrel sections that may be associated with or be part of the cutting tips as according to this invention. It is apparent that cutting edges of cutting tips  282 - 294  could be integrally formed or ground thereon or that they could be attachable whether removably so or not, despite how they are specifically illustrated in FIGS. 118-131. 
     It is apparent that the number of cutting edges per individual cutting tip i.e. attachable tip blades and/or integrally formed cutting edges such as formed at facet junctures by one or more bevels, may vary. The number of cutting edges is preferably between 1 and 7 but may include more depending on the tip design and intended use of the penetrating or cutting device. Although the preferred embodiments of this invention have predominantly illustrated a ratio of one cutting edge for each facet of a corresponding cutting tip, it is apparent that cutting tips having more than one cutting edge per facet is within the scope of this invention, especially in cutting edge arrangements other than have been disclosed herein. 
     It is to be understood that the present invention is not limited to the sole embodiments described above, as will become apparent to those skilled in the art, but encompasses the essence of all embodiments, and their legal equivalents, within the scope of the following claims.