In
geometry, a
polytope of dimension 3 (a
polyhedron) or higher is
isohedral or
face-transitive when all its
faces are the same. More specifically, all faces must be not merely
congruent but must be
transitive, i.e. must lie within the same
symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the
entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make
fair dice.