In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin...

quadrirectified 421. These polytopes are part of a family of 255 (28 − 1) convex uniform polytopes in 8 dimensions, made of uniform polytope facets and vertex...

122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named...

In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean...

5-cube, with its 32 vertices, 80 edges, and 40 square faces, and the other 40 square faces of the 5-cube become square holes. This polytope is one of 31 uniform...

7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is...

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...

In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular...

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure...

5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces. It...

convex polytopes, a distributive polytope is a convex polytope for which coordinatewise minima and maxima of pairs of points remain within the polytope. For...

mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic...

of cross-polytopes. Cartesian coordinates for the vertices of an 8-cube centered at the origin and edge length 2 are (±1,±1,±1,±1,±1,±1,±1,±1) while the...

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra...

creates another uniform polytope, called a 6-demicube, (part of an infinite family called demihypercubes), which has 12 5-demicube and 32 5-simplex facets....

geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which...

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension...

uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete...

measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The...

In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}...

convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described...

labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The Oxford English...

In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. T ¯ 9 {\displaystyle {\bar {T}}_{9}} , also (E10)...

regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...

9-space. The complete family of 2k1 polytope polytopes are: 5-cell: 201, (5 tetrahedra cells) Pentacross: 211, (32 5-cell (201) facets) 221, (72 5-simplex...

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is...

represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment...

is a convex uniform 4-polytope or 4-dimensional polytope bounded by 56 cells: 8 small rhombicuboctahedra, 16 octahedra, and 32 triangular prisms. In the...

eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets. A...

the 231. These polytopes are part of a family of 127 (or 27−1) convex uniform polytopes in seven dimensions, made of uniform polytope facets and vertex...