Dental implants are a common treatment for the replacement of a missing tooth or missing teeth.  An implant is placed into the bone in a person's jaw in a variety of fashions and using a variety of systems.  The bone and the implant adhere together in a process known as osseointegration, thus enabling a person to have a new tooth or set of teeth held into position in the jaw utilizing screws to hold them down. 
Many firms manufacture complete systems of dental implants and prosthetic components for subsequent attachment to the implant.  In a typical construction, the implant has an axially threaded hole at its top, that is, the proximal end, near the gum surface.  After the implant has integrated with the bone, the gum of the implant is opened to expose the tapped hole.  Then a transmucosal abutment is attached to the tapped hole of the implant and extends to a level above the gum or substantially to the gum surface.  The protruding free end of the abutment is constructed for attachment of a prosthesis.  For preventing rotation of the prosthesis, the protruding end of the abutment requires a non-round shape and a hexagon protrusion has been widely used.  A recessed hexagon is also popular with some systems.  The abutment also includes a central threaded hole concentric with the threaded hole of the implant and extending inward toward the jaw bone. 
A false tooth or frame is provided with a hole therethrough, known in the industry as a chimney, and a non-round recess in its base corresponds in shape to the protruding non-round cross section for the abutment.  Thereby, the crown can be connected to the abutment and relative rotation between them is prevented so long as critical contours of the abutment and the recess in the crown are maintained. 
To prevent the crown or bridge from lifting axially from the abutment, a final screw is passed into the chimney opening and engages the tapped hole in the implant by way of the abutment so as to hold the crown axially to the abutment and to the implant.  Thus, the crown cannot rotate about the abutment or implant because it is mated with the special contours on the exposed end of the abutment.  The abutment is similarly mated to the proximal or outer end of the implant.  The crown cannot pull away from the abutment when the screw has been tightened into place. 
Finally, the chimney above the screw is filled with a composite material that hardens and is shaped as part of the crown to look lie a natural tooth. 
There are many variations in construction. 
In an alternative method, the crown is attached directly to a non-round protrusion of the implant and is held directly to the implant by a gold screw without use of an intermediate abutment. 
The implant is intended to be a permanent fixture in the jaw bone.  The abutment and crown may be replaced if necessary due to damage or poor fit by gaining access to the screw head by way of the chimney, and backing off the screw so that the crown and abutment or crown to the implant can be separated from the implant.  Thus repairs may be made of an abutment and crown with no or little inconvenience. 
Therefore, the fit of an implant with the crown or frame must be perfect.  If a prosthesis is placed into the mouth and does not seat correctly, the implant or abutment can be damaged.  If an implant is damaged there are not many options for its repair.  In cases where there have been a poor fit, the screws have broken inside the abutment requiring the replacement of the abutment.  There have been cases where the screw broke inside the implant.  The implants cannot be replaced without surgically removing them.  Placing a new implant in the same spot is not an advised option. 
Among related patents disclosing dental analogs include U.S. Pat.  No.  6,142,782 of Lazarof, which shows a dental analog with annular wings.  However, the annular wings do not hinder rotating and therefore misplacement of the analog within the replica cast stone.  The annular wings of Lazarof do not intersect with the cast stone material enough to prevent rotation. 
An alternative method for making dental prostheses that does not involve making an impression of the patient's mouth has been recently introduced.  It is based on Solid Freeform Fabrication (SFF) which is an industrial prototyping technique whereby 3-D Computer Aided Design (CAD) files describing a part are used to guide the actual fabrication of a solid object by one of a variety of additive methods such as stereolithography, laminated object manufacturing, or fused deposition modelling.  U.S. Pat.  No.  6,978,188 of Christensen as well as his published patent application 2005/0133955 illustrate how CT scans or MRI scans can be substituted for CAD input to create the files necessary to drive a stereolithography system which can then be used to model human bone features.  Medical Modeling LLC has used such a method in their AccuDental™ system to create dental prostheses.  Prior to implantation of posts, a scan is made of a patient's jaw.  This data is used to create files resulting in an accurate solid translucent resin model of a patient's jaw.  Teeth and roots are rendered in a different hue to show clearly how the teeth are anchored in the jaw bone.  A dental surgeon then indicates on the jaw model where analogs are to be placed in the model and at what angle they should be inserted.  Holes are then drilled into the jaw model to accept the analogs.  A surgical guide is thermally formed on top of the implant region of the model engaging the teeth or ridge surface with a close fit and transferring the analog positions accurately.  Alternatively, computer generated surgical guides which fit onto a jaw model are used.  Surgical guide sleeves at the appropriate angle are then bonded at the analog sites onto the surgical guide.  The surgical guide is snapped off the teeth or ridge surface of the model and will be transferred to the patient's mouth and snapped onto the actual teeth or the ridge surface thereby providing accurate guides for drilling the holes for the actual implants while at a remote lab, the prosthesis is being fabricated using the analogs in the jaw model.  Surgical guides fit not only on teeth, but can be used on totally edentulous jaws as well engaging soft tissue or bone surface as represented on the jaw model and on the actual patient jaw.