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

In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. Here, "vertex-transitive" means...

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...

a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope...

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

In four-dimensional geometry, a prismatic uniform 4-polytope is a uniform 4-polytope with a nonconnected Coxeter diagram symmetry group.[citation needed]...

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

polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets. A uniform 9-polytope...

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...

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 elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any...

8-polytope ridge. A uniform 10-polytope is one which is vertex-transitive, and constructed from uniform facets. Regular 10-polytopes can be represented...

In 4-dimensional geometry, a uniform antiprismatic prism or antiduoprism is a uniform 4-polytope with two uniform antiprism cells in two parallel 3-space...

considered to be prismatic 4-polytopes. A duoprism constructed from two regular polygons of the same edge length is a uniform duoprism. A duoprism made...

In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset...

six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional figure...

hyperbolic 3-space. uniform polyhedron uniform 4-polytope Rectification (geometry) Truncation (geometry) Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973)...

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 uniform 8-polytope...

runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 120-cell. There are 4 degrees of runcinations...

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin...

In four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell...

geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge...

higher-dimensional polytopes and tessellations. All uniform polytopes are isogonal, for example, the uniform 4-polytopes and convex uniform honeycombs. The...

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 four-dimensional geometry, a cantellated 120-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 120-cell...

In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell. There are two...

the 5-polytope Edge the (n−4)-face of the 5-polytope Face the peak or (n−3)-face of the 5-polytope Cell the ridge or (n−2)-face of the 5-polytope Hypercell...

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge...

convex uniform polytopes used in uniform polyhedron, uniform 4-polytope, uniform 5-polytope, uniform 6-polytope, uniform tiling, and convex uniform honeycomb...

antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and...