Chiral polytope

This article is about polytopes with full rotational symmetry. For polytopes lacking mirror symmetry see, see Chirality.
The flags of Heawood map under its automorphism group form two orbits, colored here in black and yellow.

In the study of abstract polytopes, a chiral polytope is a polytope that is as symmetric as possible without being mirror-symmetric, formalized in terms of the action of the symmetry group of the polytope on its flags.