Isohedral figure

≥2-dimensional tessellation or ≥3-dimensional polytope with identical faces

In geometry, a tessellation of dimension 2 or higher, or a polytope of dimension 3 or higher, is isohedral or face-transitive if 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 two faces A and B, there must be a symmetry of the entire figure by translations, rotations, and/or reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.

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