1. A method of creating a prosthetic tooth to be placed on a dental implant, comprising: receiving scan data from a patient's mouth, the scan data including information about the location of the dental implant installed in the patient's mouth; using a computer, developing a computer model of the patient's mouth from the scan data; by use of the computer model, developing a first data set to be used in developing a rapid-prototype physical model, the rapid-prototype physical model having a receptacle for receiving an implant analog at a location corresponding to the implant installed in the patient's mouth; providing the implant analog to be placed in the receptacle of the rapid-prototype physical model, the implant analog having features corresponding to the installed dental implant; by use of the computer model, developing a second data set to be used in developing a custom dental abutment to be placed on the dental implant in the patient's mouth; and manufacturing the custom dental abutment by use of the second data set, the custom dental abutment to be attached to the implant analog after the implant analog has been installed in the receptacle in the rapid-prototype physical model so as to allow for the fabrication of a tooth-like restoration on the custom dental abutment, the prosthetic tooth comprising the tooth-like restoration and the custom dental abutment.