Runcinated 5orthoplexes
In fivedimensional geometry, a runcinated 5orthoplex is a convex uniform 5polytope with 3rd order truncation of the regular 5orthoplex. There are 8 runcinations of the 5orthoplex with permutations of truncations, and cantellations. Four are ...
Runcinated 5simplexes
In sixdimensional geometry, a runcinated 5simplex is a convex uniform 5polytope with 3rd order truncations of the regular 5simplex. There are 4 unique runcinations of the 5simplex with permutations of truncations, and cantellations.
Steric 5cubes
In fivedimensional geometry, a steric 5cube or is a convex uniform 5polytope. There are unique 4 steric forms of the 5cube. Steric 5cubes have half the vertices of stericated 5cubes.
Stericated 5cubes
In fivedimensional geometry, a stericated 5cube is a convex uniform 5polytope with fourthorder truncations of the regular 5cube. There are eight degrees of sterication for the 5cube, including permutations of runcination, cantellation, and ...
Stericated 5simplexes
In fivedimensional geometry, a stericated 5simplex is a convex uniform 5polytope with fourthorder truncations of the regular 5simplex. There are six unique sterications of the 5simplex, including permutations of truncations, cantellations, ...
Truncated 5cubes
In fivedimensional geometry, a truncated 5cube is a convex uniform 5polytope, being a truncation of the regular 5cube. There are four unique truncations of the 5cube. Vertices of the truncated 5cube are located as pairs on the edge of the 5 ...
Truncated 5orthoplexes
In sixdimensional geometry, a truncated 5orthoplex is a convex uniform 5polytope, being a truncation of the regular 5orthoplex. There are 4 unique truncations of the 5orthoplex. Vertices of the truncation 5orthoplex are located as pairs on ...
Truncated 5simplexes
In fivedimensional geometry, a truncated 5simplex is a convex uniform 5polytope, being a truncation of the regular 5simplex. There are unique 2 degrees of truncation. Vertices of the truncation 5simplex are located as pairs on the edge of th ...
Uniform 5polytope
In geometry, a uniform 5polytope is a fivedimensional uniform polytope. By definition, a uniform 5polytope is vertextransitive and constructed from uniform 4polytope facets. The complete set of convex uniform 5polytopes has not been determi ...
6polytope
A 6polytope is a closed sixdimensional figure with vertices, edges, faces, cells 3faces, 4faces, and 5faces. 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 6dimensional 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 6dimensional geometry, the 2 21 polytope is a uniform 6polytope, constructed within the symmetry of the E 6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6ic semiregular figure. It is also called ...
6cube
In geometry, a 6cube is a sixdimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4faces, and 12 5cube 5faces. It has Schlafli symbol {4.3 4 }, being composed of 3 5cubes around each 4face. It ...
6demicube
In geometry, a 6demicube or demihexteract is a uniform 6polytope, constructed from a 6cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in ...
6orthoplex
In geometry, a 6orthoplex, or 6cross polytope, is a regular 6polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5cell 4faces, and 64 5faces. It has two constructed forms, the first being regular with Schlafl ...
6simplex
In geometry, a 6simplex is a selfdual regular 6polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5cell 4faces, and 7 5simplex 5faces. Its dihedral angle is cos −1, or approximately 80.41°.
A6 polytope
In 6dimensional geometry, there are 35 uniform polytopes with A 6 symmetry. There is one selfdual regular form, the 6simplex with 7 vertices. Each can be visualized as symmetric orthographic projections in Coxeter planes of the A 6 Coxeter gro ...
B6 polytope
In 6dimensional geometry, there are 64 uniform polytopes with B 6 symmetry. There are two regular forms, the 6orthoplex, and 6cube with 12 and 64 vertices respectively. The 6demicube is added with half the symmetry. They can be visualized as ...
Cantellated 6cubes
In sixdimensional geometry, a cantellated 6cube is a convex uniform 6polytope, being a cantellation of the regular 6cube. There are 8 cantellations for the 6cube, including truncations. Half of them are more easily constructed from the dual ...
Cantellated 6orthoplexes
In sixdimensional geometry, a cantellated 6orthoplex is a convex uniform 6polytope, being a cantellation of the regular 6orthoplex. There are 8 cantellation for the 6orthoplex including truncations. Half of them are more easily constructed f ...
Cantellated 6simplexes
In sixdimensional geometry, a cantellated 6simplex is a convex uniform 6polytope, being a cantellation of the regular 6simplex. There are unique 4 degrees of cantellation for the 6simplex, including truncations.
Cantic 6cube
The Cartesian coordinates for the 480 vertices of a cantic 6cube 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 6dimensional 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 6orthoplex, and 6demicube with 12 and 32 vertices respectively. They can be vi ...
E6 polytope
In 6dimensional 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 6cubes
In sixdimensional geometry, a pentellated 6cube is a convex uniform 6polytope with 5th order truncations of the regular 6cube. There are unique 16 degrees of pentellations of the 6cube with permutations of truncations, cantellations, runcina ...
Pentellated 6orthoplexes
In sixdimensional geometry, a pentellated 6orthoplex is a convex uniform 6polytope with 5th order truncations of the regular 6orthoplex. There are unique 16 degrees of pentellations of the 6orthoplex with permutations of truncations, cantell ...
Pentellated 6simplexes
In sixdimensional geometry, a pentellated 6simplex is a convex uniform 6polytope with 5th order truncations of the regular 6simplex. There are unique 10 degrees of pentellations of the 6simplex with permutations of truncations, cantellations ...
Pentic 6cubes
The Cartesian coordinates for the vertices of a pentic 6cube centered at the origin are coordinate permutations: ±1,±1,±1,±1,±1,±3 with an odd number of plus signs.
Rectified 6cubes
In sixdimensional geometry, a rectified 6cube is a convex uniform 6polytope, being a rectification of the regular 6cube. There are unique 6 degrees of rectifications, the zeroth being the 6cube, and the 6th and last being the 6orthoplex. Ve ...
Rectified 6orthoplexes
In sixdimensional geometry, a rectified 6orthoplex is a convex uniform 6polytope, being a rectification of the regular 6orthoplex. There are unique 6 degrees of rectifications, the zeroth being the 6orthoplex, and the 6th and last being the ...
Rectified 6simplexes
In sixdimensional geometry, a rectified 6simplex is a convex uniform 6polytope, being a rectification of the regular 6simplex. There are three unique degrees of rectifications, including the zeroth, the 6simplex itself. Vertices of the recti ...
Runcic 6cubes
The Cartesian coordinates for the vertices of a runcic 6cube centered at the origin are coordinate permutations: ±1,±1,±1,±3,±3,±3 with an odd number of plus signs.
Runcinated 6cubes
In sixdimensional geometry, a runcinated 6cube is a convex uniform 6polytope with 3rd order truncations of the regular 6cube. There are 12 unique runcinations of the 6cube with permutations of truncations, and cantellations. Half are express ...
Runcinated 6orthoplexes
In sixdimensional geometry, a runcinated 6orthplex is a convex uniform 6polytope with 3rd order truncations of the regular 6orthoplex. There are 12 unique runcinations of the 6orthoplex with permutations of truncations, and cantellations. Ha ...
Runcinated 6simplexes
In sixdimensional geometry, a runcinated 6simplex is a convex uniform 6polytope constructed as a runcination of the regular 6simplex. There are 8 unique runcinations of the 6simplex with permutations of truncations, and cantellations.
Steric 6cubes
The Cartesian coordinates for the 480 vertices of a steric 6cube centered at the origin are coordinate permutations: ±1,±1,±1,±1,±1,±3 with an odd number of plus signs.
Stericated 6cubes
In sixdimensional geometry, a stericated 6cube is a convex uniform 6polytope, constructed as a sterication of the regular 6cube. There are 8 unique sterications for the 6cube with permutations of truncations, cantellations, and runcinations.
Stericated 6orthoplexes
In sixdimensional geometry, a stericated 6orthoplex is a convex uniform 6polytope, constructed as a sterication of the regular 6orthoplex. There are 16 unique sterications for the 6orthoplex with permutations of truncations, cantellations, a ...
Stericated 6simplexes
In sixdimensional geometry, a stericated 6simplex is a convex uniform 6polytope with 4th order truncations of the regular 6simplex. There are 8 unique sterications for the 6simplex with permutations of truncations, cantellations, and runcina ...
Truncated 6cubes
In sixdimensional geometry, a truncated 6cube is a convex uniform 6polytope, being a truncation of the regular 6cube. There are 5 truncations for the 6cube. Vertices of the truncated 6cube are located as pairs on the edge of the 6cube. Ver ...
Truncated 6orthoplexes
In sixdimensional geometry, a truncated 6orthoplex is a convex uniform 6polytope, being a truncation of the regular 6orthoplex. There are 5 degrees of truncation for the 6orthoplex. Vertices of the truncated 6orthoplex are located as pairs ...
Truncated 6simplexes
In sixdimensional geometry, a truncated 6simplex is a convex uniform 6polytope, being a truncation of the regular 6simplex. There are unique 3 degrees of truncation. Vertices of the truncation 6simplex are located as pairs on the edge of the ...
Uniform 6polytope
In sixdimensional geometry, a uniform polypeton is a sixdimensional uniform polytope. A uniform polypeton is vertextransitive, and all facets are uniform 5polytopes. The complete set of convex uniform polypeta has not been determined, but mos ...
1 32 polytope
In 7dimensional geometry, 1 32 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 1 32, describing its bifurcating CoxeterDynkin diagram, with a single ring on the end of one of the 1node sequences. The rectified 1 32 ...
2 22 honeycomb
In geometry, the 22 honeycomb is a uniform tessellation of the sixdimensional 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 7dimensional geometry, 2 31 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 2 31, describing its bifurcating CoxeterDynkin diagram, with a single ring on the end of the 2node branch. The rectified 2 31 is constru ...
3 21 polytope
In 7dimensional geometry, the 3 21 polytope is a uniform 7polytope, constructed within the symmetry of the E 7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 7ic semiregular figure. Its Coxeter symbol ...
7cube
In geometry, a 7cube is a sevendimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4faces, 84 penteract 5faces, and 14 hexeract 6faces. It can be named by its Schlafli symbol {4.3 5 }, being c ...
7demicube
In geometry, a demihepteract or 7demicube is a uniform 7polytope, constructed from the 7hypercube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified ...
7orthoplex
In geometry, a 7orthoplex, or 7cross polytope, is a regular 7polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5cells 4faces, 448 5faces, and 128 6faces. It has two constructed forms, the first being regul ...
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7simplex 

A7 polytope 

B7 polytope 

Cantellated 7cubes 

Cantellated 7orthoplexes 

Cantellated 7simplexes 

Cantic 7cube 

D7 polytope 

E7 polytope 

Hexic 7cubes 

Hexicated 7cubes 

Hexicated 7simplexes 

Pentellated 7cubes 

Pentellated 7orthoplexes 

Pentellated 7simplexes 

Pentic 7cubes 
Rectified 7cubes 
Rectified 7orthoplexes 

Rectified 7simplexes 

Runcic 7cubes 

Runcinated 7cubes 

Runcinated 7orthoplexes 

Runcinated 7simplexes 

Steric 7cubes 

Stericated 7cubes 

Stericated 7orthoplexes 

Stericated 7simplexes 
Truncated 7cubes 

Truncated 7orthoplexes 

Truncated 7simplexes 

Uniform 7polytope 
1 33 honeycomb 

1 42 polytope 

2 41 polytope 
3 31 honeycomb 

4 21 polytope 

8cube 

8demicube 

8orthoplex 

Uniform 8polytope 

8simplex 

A8 polytope 

B8 polytope 

Cantellated 8simplexes 

Cantic 8cube 

D8 polytope 

E8 polytope 

Heptellated 8simplexes 

Hexicated 8simplexes 

Pentellated 8simplexes 

Rectified 8cubes 
Rectified 8orthoplexes 

Rectified 8simplexes 
Runcinated 8simplexes 

Stericated 8simplexes 
Truncated 8cubes 
Truncated 8orthoplexes 

Truncated 8simplexes 
1 52 honeycomb 
2 51 honeycomb 
5 21 honeycomb 

9cube 

9demicube 

9orthoplex 

9simplex 

Rectified 9cubes 
Rectified 9orthoplexes 

Rectified 9simplexes 

Uniform 9polytope 

10cube 

10demicube 

10orthoplex 

10simplex 
E9 honeycomb 

Rectified 10cubes 

Rectified 10orthoplexes 

Rectified 10simplexes 

Uniform 10polytope 

Biregular graph 

Intersection graph 

Polygoncircle graph 

Barbell graph 

Bouquet graph 
Cocktail party graph 

Complete bipartite graph 

Half graph 

Pancake graph 
Shannon multigraph 
Godel operation 
Jensen hierarchy 
Minimal model (set theory) 

Silver machine 

Pythagorean interval 

List of intervals in 5limit just int .. 

Fivelimit tuning 

7limit tuning 
Undecimal minor sixth 
Tridecimal minor third 
Tridecimal neutral seventh 
Tridecimal neutral third 
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