## Runcinated 5-orthoplexes

In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation of the regular 5-orthoplex. There are 8 runcinations of the 5-orthoplex with permutations of truncations, and cantellations. Four are ...

## Runcinated 5-simplexes

In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations of the regular 5-simplex. There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations.

## Steric 5-cubes

In five-dimensional geometry, a steric 5-cube or is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.

## Stericated 5-cubes

In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations of the regular 5-cube. There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and ...

## Stericated 5-simplexes

In five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations of the regular 5-simplex. There are six unique sterications of the 5-simplex, including permutations of truncations, cantellations, ...

## Truncated 5-cubes

In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube. There are four unique truncations of the 5-cube. Vertices of the truncated 5-cube are located as pairs on the edge of the 5 ...

## Truncated 5-orthoplexes

In six-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on ...

## Truncated 5-simplexes

In five-dimensional geometry, a truncated 5-simplex is a convex uniform 5-polytope, being a truncation of the regular 5-simplex. There are unique 2 degrees of truncation. Vertices of the truncation 5-simplex are located as pairs on the edge of th ...

## Uniform 5-polytope

In geometry, 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 facets. The complete set of convex uniform 5-polytopes has not been determi ...

## 6-polytope

A 6-polytope is a closed six-dimensional figure with vertices, edges, faces, cells 3-faces, 4-faces, and 5-faces. A vertex is a point where six or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon w ...

## 1 22 polytope

In 6-dimensional geometry, the 1 22 polytope is a uniform polytope, constructed from the E 6 group. It was first published in E. L. Eltes 1912 listing of semiregular polytopes, named as V 72. Its Coxeter symbol is 1 22, describing its bifurcating ...

## 2 21 polytope

In 6-dimensional geometry, the 2 21 polytope is a uniform 6-polytope, constructed within the symmetry of the E 6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure. It is also called ...

## 6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces. It has Schlafli symbol {4.3 4 }, being composed of 3 5-cubes around each 4-face. It ...

## 6-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in ...

## 6-orthoplex

In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces. It has two constructed forms, the first being regular with Schlafl ...

## 6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and 7 5-simplex 5-faces. Its dihedral angle is cos −1, or approximately 80.41°.

## A6 polytope

In 6-dimensional geometry, there are 35 uniform polytopes with A 6 symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices. Each can be visualized as symmetric orthographic projections in Coxeter planes of the A 6 Coxeter gro ...

## B6 polytope

In 6-dimensional geometry, there are 64 uniform polytopes with B 6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices respectively. The 6-demicube is added with half the symmetry. They can be visualized as ...

## Cantellated 6-cubes

In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube. There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual ...

## Cantellated 6-orthoplexes

In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex. There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed f ...

## Cantellated 6-simplexes

In six-dimensional geometry, a cantellated 6-simplex is a convex uniform 6-polytope, being a cantellation of the regular 6-simplex. There are unique 4 degrees of cantellation for the 6-simplex, including truncations.

## Cantic 6-cube

The Cartesian coordinates for the 480 vertices of a cantic 6-cube centered at the origin and edge length 6 √ 2 are coordinate permutations: ±1,±1,±3,±3,±3,±3 with an odd number of plus signs.

## D6 polytope

In 6-dimensional geometry, there are 47 uniform polytopes with D 6 symmetry, 16 are unique, and 31 are shared with the B 6 symmetry. There are two regular forms, the 6-orthoplex, and 6-demicube with 12 and 32 vertices respectively. They can be vi ...

## E6 polytope

In 6-dimensional geometry, there are 39 uniform polytopes with E 6 symmetry. The two simplest forms are the 2 21 and 1 22 polytopes, composed of 27 and 72 vertices respectively. They can be visualized as symmetric orthographic projections in Coxe ...

## Pentellated 6-cubes

In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube. There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcina ...

## Pentellated 6-orthoplexes

In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex. There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantell ...

## Pentellated 6-simplexes

In six-dimensional geometry, a pentellated 6-simplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-simplex. There are unique 10 degrees of pentellations of the 6-simplex with permutations of truncations, cantellations ...

## Pentic 6-cubes

The Cartesian coordinates for the vertices of a pentic 6-cube centered at the origin are coordinate permutations: ±1,±1,±1,±1,±1,±3 with an odd number of plus signs.

## Rectified 6-cubes

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube. There are unique 6 degrees of rectifications, the zeroth being the 6-cube, and the 6th and last being the 6-orthoplex. Ve ...

## Rectified 6-orthoplexes

In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex. There are unique 6 degrees of rectifications, the zeroth being the 6-orthoplex, and the 6th and last being the ...

## Rectified 6-simplexes

In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex. There are three unique degrees of rectifications, including the zeroth, the 6-simplex itself. Vertices of the recti ...

## Runcic 6-cubes

The Cartesian coordinates for the vertices of a runcic 6-cube centered at the origin are coordinate permutations: ±1,±1,±1,±3,±3,±3 with an odd number of plus signs.

## Runcinated 6-cubes

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations of the regular 6-cube. There are 12 unique runcinations of the 6-cube with permutations of truncations, and cantellations. Half are express ...

## Runcinated 6-orthoplexes

In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations of the regular 6-orthoplex. There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. Ha ...

## Runcinated 6-simplexes

In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination of the regular 6-simplex. There are 8 unique runcinations of the 6-simplex with permutations of truncations, and cantellations.

## Steric 6-cubes

The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations: ±1,±1,±1,±1,±1,±3 with an odd number of plus signs.

## Stericated 6-cubes

In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication of the regular 6-cube. There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.

## Stericated 6-orthoplexes

In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication of the regular 6-orthoplex. There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, a ...

## Stericated 6-simplexes

In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations of the regular 6-simplex. There are 8 unique sterications for the 6-simplex with permutations of truncations, cantellations, and runcina ...

## Truncated 6-cubes

In six-dimensional geometry, a truncated 6-cube is a convex uniform 6-polytope, being a truncation of the regular 6-cube. There are 5 truncations for the 6-cube. Vertices of the truncated 6-cube are located as pairs on the edge of the 6-cube. Ver ...

## Truncated 6-orthoplexes

In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex. There are 5 degrees of truncation for the 6-orthoplex. Vertices of the truncated 6-orthoplex are located as pairs ...

## Truncated 6-simplexes

In six-dimensional geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex. There are unique 3 degrees of truncation. Vertices of the truncation 6-simplex are located as pairs on the edge of the ...

## Uniform 6-polytope

In six-dimensional geometry, a uniform polypeton is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform polypeta has not been determined, but mos ...

## 1 32 polytope

In 7-dimensional geometry, 1 32 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 1 32, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 1-node sequences. The rectified 1 32 ...

## 2 22 honeycomb

In geometry, the 22 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schlafli symbol {3.3.3 2.2 }. It is constructed from 2 21 facets and has a 1 22 vertex figure, with 54 2 21 polytopes aro ...

## 2 31 polytope

In 7-dimensional geometry, 2 31 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 2 31, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node branch. The rectified 2 31 is constru ...

## 3 21 polytope

In 7-dimensional geometry, the 3 21 polytope is a uniform 7-polytope, constructed within the symmetry of the E 7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 7-ic semi-regular figure. Its Coxeter symbol ...

## 7-cube

In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces. It can be named by its Schlafli symbol {4.3 5 }, being c ...

## 7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified ...

## 7-orthoplex

In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cells 4-faces, 448 5-faces, and 128 6-faces. It has two constructed forms, the first being regul ... 