Isohedral figure

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.

A form that is isohedral, has regular vertices, and is also edge-transitive (i.e. isotoxal) is said to be a quasiregular dual.

[7] Here are some examples of k-isohedral polyhedra and tilings, with their faces colored by their k symmetry positions: A cell-transitive or isochoric figure is an n-polytope (n ≥ 4) or n-honeycomb (n ≥ 3) that has its cells congruent and transitive with each others.

[8] A facet-transitive or isotopic figure is an n-dimensional polytope or honeycomb with its facets ((n−1)-faces) congruent and transitive.