A d-polytope with 2n vertices is equi-partite if for every set of n vertices there is an isometry of the polytope that maps them onto the other n vertices. Similarly, a graph of order 2n is equi-partite if for every choice of n vertices the subgraph spanned by them is isomorphic to the subgraph spanned by the other n vertices.

Using a complete characterization of equi-partite graphs we identify all equivalence d-polyphase. We also prove that the maximum number of vertices in an equi-partite d-polygon is 2d+2.

Joint work with B. Grunbaum, T. Kaiser, D. Kral and M. Rosenfeld