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.
In the study of abstract polytopes, a chiralpolytope is a polytope that is as symmetric as possible without being mirror-symmetric, formalized in terms...
mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...
In the latter paper, Pasteur sketches from natural concrete reality chiralpolytopes quite possibly for the first time. The optical property of tartaric...
examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Convex polyhedra are...
regular polytopes. Coxeter lists a few of these in his book Regular Polytopes. McMullen added six in his paper New Regular Compounds of 4-Polytopes. Self-duals:...
octahedron is the three-dimensional case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric. If the...
In 4-dimensional geometry, there are 9 uniform 4-polytopes with F4 symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular...
polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure...
polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for each with half the order, and...
face-to-face in a chiral aperiodic chain called the Boerdijk–Coxeter helix. In four dimensions, all the convex regular 4-polytopes with tetrahedral cells...
regular polytopes. Extended symmetries exist in uniform polychora with symmetric ring-patterns within the Coxeter diagram construct. Chiral symmetries...
on the comparison mensuration. It also has many relations with other polytopes. The appearance of regular icosahedron can be found in nature, such as...
pentagon-tritetrahedron, and tetrahedric pentagon dodecahedron) is a dodecahedron with chiral tetrahedral symmetry (T). Like the regular dodecahedron, it has twelve identical...
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