We consider partitional clustering methods for n objects with a fixed number m of classes. It is well-known that suitable clustering criteria can be obtained in the framework of probabilistic models that assume class-specific distributions for n random vectors X1, ...,Xn in Rp . This paper proposes three special clustering models where each of the underlying classes C1, ...,Cm from {1, ...,n}is characterized by a uniform distribution U(Ki) on a convex and finite domain Ki of Rp. We derive the corresponding clustering criteria for determining the unknown classes Ci and domains Ki and the maximum likedlihood ratio test statistics for testing the existence of such clustering structures in the observed data. All criteria are based on the determination of convex hulls of data points in Rp.