A heretofore unsolved problem of great archaeological importance is the automatic assembly of pots made on a wheel from the hundreds (or thousands) of sherds found at an excavation site. An approach is presented to the automatic estimation of mathematical models of such pots from 3D measurements of sherds. The overall approach is formulated and described and some detail is provided on the elements of the procedure. The end result is a representation suitable for comparisons, geometric feature extraction, visualization and digital archiving. Matching of fragments and aligning them geometrically is based on matching break-curves (curves on a pot surface separating fragments), estimated axes and profile curves for individual fragments and groups of matched fragments, and a number of features of groups of break-curves. Pot assembly is a bottom-up maximum likelihood performance-based search. In our case, associated with subassemblies of fragments is a loglikelihood which is a sum of energy functions. Experiments are illustrated on pots which were broken for the purpose, and on sherds from an archaeological dig located in Petra, Jordan. The addressed problem and solution can be considered as problems in "geometric learning" and in "perceptual grouping," where subgroups of pot fragments at a site location are to be assembled into individual virtual pots and other fragments are to be discarded as clutter.