Cell-transitive

From Wikipedia, the free encyclopedia

In geometry, a polytope is isochoric or cell-transitive when all its cells are the same.

More specifically, all cells (of all dimensions) must be not merely abstractly congruent but must be transitive, i.e. must lie within the same symmetry orbit. For a polyhedron, cell-transitive is equivalent to being at once vertex-transitive (transitive on 0-cells), edge-transitive (transitive on 1-cells), and face-transitive (transitive on 2-cells).

A polytope that is flag-transitive is automatically cell-transitive.

All regular polychora and honeycombs are cell-transitive, as well as the self-dual bitruncated uniform polychoron and uniform honeycombs. In addition, all duals to the uniform polychora and honeycombs are cell-transitive.

[edit] See also

• Vertex-transitive
• Edge-transitive
• Face-transitive