1. A system for use in fabricating dental appliances, said system comprising: a processor operably coupled to a computer readable storage medium comprising instructions that, when executed, cause the processor to: receive a virtual three dimensional (3D) representation of a patient's lower arch, the patient's upper arch, and an occlusion alignment between the upper and lower arches, and modify the virtual 3D representation by adding a first virtual alignment structure to the lower arch and a second virtual alignment structure to the upper arch, the first and second virtual alignment structures shaped to engage each other to produce the occlusion alignment between the upper and lower arches; and a physical model of the dentition comprising, a lower arch model having lower teeth and an upper arch model having upper teeth, said physical model based on the modified virtual 3D representation, a first single continuous piece comprising the lower arch model and a first alignment structure extending from and integrally formed with the lower arch model, the first alignment structure shaped according to the first virtual alignment structure, and a second single continuous piece comprising the upper arch model and a second alignment structure extending from and integrally formed with the upper arch model, the second alignment structure shaped according to the second virtual alignment structure, wherein one or more of a first plurality of first positioning reference components or a second plurality of second positioning reference components are formed to allow the first plurality of first positioning reference components to come into reversible contact with the second plurality of second positioning reference components in a fixed spatial relationship to thereby provide the occlusion alignment between the lower teeth of the lower arch model and the upper teeth of the upper arch model based on said modified virtual 3D representation.