Runcinated 5orthoplexes
In fivedimensional geometry, a runcinated 5orthoplex is a convex shape 5polytope with 3rd order truncations of the regular 5orthoplex. There are 8 runcinations of 5orthoplex with permutations of truncations, and cantellations. Four more simp ...
Runcinated 5simplexes
In sixdimensional geometry, a runcinated 5simplex is a convex uniform 5polytope with 3rd order truncation of the regular 5simplex. There are 4 unique runcinations of the 5simplex with permutations of truncations, and cantellations.
Steric 5cubes
In fivedimensional geometry, steric 5cube or convex uniform 5polytope. There are 4 unique forms of steric 5cube. Steric 5cubes have half the vertices stericated 5cube.
Stericated 5cubes
In fivedimensional geometry, stericated 5cube is a convex uniform 5polytope with fourthorder truncation of the regular 5cube. There are eight degrees sterication for the 5cube, including permutations runcination, cantellation, and truncatio ...
Stericated 5simplexes
In fivedimensional geometry, stericated 5simplex is a convex uniform 5polytope with fourthorder truncation of the regular 5simplex. six unique sterications of the 5simplex, including permutations of truncation, cantellations, and runcinatio ...
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 a truncated 5cube are located as pairs on the edge of a 5cub ...
Truncated 5orthoplexes
In sixdimensional geometry, a truncated 5orthoplex is a convex shape 5polytope, being a truncation of the regular 5orthoplex. There are 4 unique truncation at the 5orthoplex. The top of the truncated 5orthoplex are located as pairs on the e ...
Truncated 5simplexes
In fivedimensional geometry, a truncated 5simplex is a convex uniform 5polytope, being a truncation of the regular 5simplex. There are 2 unique degrees of truncation. The top of the truncated 5simplex are located in pairs on the edge of a 5 ...
Uniform 5polytope
In geometry, a uniform 5polytope, is a fivedimensional Uniform polytope. By definition, a uniform 5polytope vertices, transitive and constructed from uniform 4polytope facets. A complete set of convex uniform 5polytopes have not yet been det ...
6polytope
6polyhedron is a closed sixdimensional figure with vertices, edges, faces, cells, 3facade, 4faces and 5faces. A vertex is a point where six or more faces. An edge is a segment where four or more faces meet, and the face is a polygon where th ...
1 22 polytope
In 6dimensional geometry, 1 22 polytope is a uniform polytope, constructed from the e6 group. It was first published in E. L. Eltes 1912 list of semiregular polytopes, named 72. Its Coxeter symbol is 1 22, describing its branching CoxeterDynki ...
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 paper of 1900. He called his 6IC semiregular figure. It is also called ...
6cube
In geometry, a 6cube is a sixdimensional hypercube with 64 vertices, 192 edges, 240 square meters of the Facade, 160 cubic cells, 60 Tesseract 4faces, and 12 55 cubefaces. It has Schlafli symbol {4 4.3 }, consisting of 3 5cubes around each ...
6demicube
In geometry, a 6demicube or demihexteract uniform 6polytope, consisting of a 6cube with alternated vertices deleted. It is part of a multidimensional infinite family of uniform polytopes called demihypercubes. E. L. ELTE identified it in 1912 ...
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 of which regularly with Sc ...
6simplex
In geometry, a 6simplex is a dual regular 6polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5cell 4faces, and 7 55 simplex face. Its dihedral angle, cos 1, or approximately 80.41°.
A6 polytope
In 6dimensional geometry, there are 35 homogeneous polyhedra with 6 symmetry. There is one selfdual regular form, the 6Simplex with 7 vertices. Each can be represented as symmetric orthographic projections in Coxeter planes of the 6 Coxeter gr ...
B6 polytope
In 6dimensional geometry, there are 64 uniform polyhedra with B 6 symmetry. There are two normal forms, a 6orthoplex, and a 6cube with 12 and 64 vertices respectively. 6demicube is added with half symmetry. They can be visualized as symmetric ...
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 more simple design with dual 5orthoplex.
Cantellated 6orthoplexes
In sixdimensional geometry, a cantellated 6orthoplex is a convex shape 6polytope, being a cantellation of the regular 6orthoplex. There are 8 cantellation for the 6orthoplex including truncations. Half of them more simple design with dual 5cube
Cantellated 6simplexes
In sixdimensional geometry, a cantellated 6simplex is a convex uniform 6polytope, being a cantellation of the regular 6simplex. There is a unique 4 degrees of cantellation for the 6simplex, including truncations.
Cantic 6cube
Cartesian coordinates for the 480 vertices cantic 6cube with center 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 together with B 6 symmetry. There are two normal forms, a 6orthoplex, and 6demicube with 12 and 32 peaks, respectively. They can be visualized as ...
E6 polytope
In 6dimensional geometry, a 39 homogeneous polyhedra With E 6 symmetry. The two most simple forms 2 and 21, 22 1 polytopes, composed of 27 and 72 vertices, respectively. They can be visualized as symmetric orthographic projections in Coxeter pla ...
Pentellated 6cubes
In sixdimensional geometry, pentellated 6cube is a convex uniform 6polytope with 5th order truncation of the regular 6cube. There are unique 16 degrees pentellations of the 6cube with permutations of truncation, cantellations, runcinations, ...
Pentellated 6orthoplexes
In sixdimensional geometry, pentellated 6orthoplex is a convex form 6polytope with 5th order truncation of the regular 6orthoplex. There are unique 16 degrees pentellations of the 6orthoplex with permutations of truncation, cantellations, ru ...
Pentellated 6simplexes
In sixdimensional geometry, pentellated 6simplex is a convex uniform 6polytope with 5th order truncation of the regular 6simplex. There are unique 10 degrees pentellations of the 6simplex with permutations of truncation, cantellations, runci ...
Pentic 6cubes
Cartesian coordinates of the vertices of a pentic 6cube with center at the origin of 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 refinements, zero being the 6cube, and the 6th and last being the 6orthoplex. Vertices of ...
Rectified 6orthoplexes
In sixdimensional geometry, a rectified 6orthoplex is a convex shape 6polytope, being a rectification of the regular 6orthoplex. There are unique 6 degrees of refinements, zero being the 6orthoplex, and the 6th and last being the 6cube. Ver ...
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 correction, including a zero, a 6simplex itself. Vertices of the rectified 6sim ...
Runcic 6cubes
Cartesian coordinates of the vertices runcic 6cube with center at the origin of 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 truncation of the regular 6cube. There are 12 unique runcinations of the 6cube with permutations of truncations, and cantellations. Half expressed in ...
Runcinated 6orthoplexes
In sixdimensional geometry, a runcinated 6orthplex is a convex uniform 6polytope with 3rd order truncation of the regular 6orthoplex. There are 12 unique runcinations of the 6orthoplex with permutations of truncations, and cantellations. Hal ...
Runcinated 6simplexes
In sixdimensional geometry, a runcinated 6simplex is a convex uniform 6polytope, constructed as runcination regular 6simplex. There are 8 unique runcinations of the 6simplex with permutations of truncations, and cantellations.
Steric 6cubes
Cartesian coordinates for the 480 vertices of a steric 6cube with center at the origin of coordinate permutations: ±1,±1,±1,±1,±1,±3 with an odd number of plus signs.
Stericated 6cubes
In sixdimensional geometry, stericated 6cube is a convex uniform 6polytope, constructed as sterication regular 6cube. There are 8 unique sterications for the 6cube with permutations of truncation, cantellations, and runcinations.
Stericated 6orthoplexes
In sixdimensional geometry, stericated 6orthoplex is a convex shape 6polytope, constructed as sterication regular 6orthoplex. There are 16 unique sterications for the 6orthoplex with permutations of truncation, cantellations, and runcination ...
Stericated 6simplexes
In sixdimensional geometry, stericated 6simplex is a convex uniform 6polytope with 4th order truncation of the regular 6simplex. There are 8 unique sterications for the 6simplex with permutations of truncation, cantellations, and runcinations.
Truncated 6cubes
In sixdimensional geometry, a truncated 6cube is a convex uniform 6polytope, being a truncation of the regular 6cube. There are 5 truncation 6cubic Vertices of the truncated 6cube are located as pairs on the edge of the 6cubic vertices of ...
Truncated 6orthoplexes
In sixdimensional geometry, a truncated 6orthoplex is a convex shape 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 on ...
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. The vertices of the truncated 6simplex are located in pairs on the edge of ...
Uniform 6polytope
In sixdimensional geometry, a uniform polypeton is a sixdimensional uniform polytope. Single polypeton is vertextransitive, and all the facets are uniform 5polytopes. A complete set of convex uniform polypeta not yet determined, but most of t ...
1 32 polytope
In 7dimensional geometry, 1 32 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is a 1 32, describing its branching CoxeterDynkin diagram, with a single ring on the end of one of the 1node sequences. Rectified 1 32 is c ...
2 22 honeycomb
In geometry, 22 Honeycomb tessellation in a Single sixdimensional Euclidean space. It can be represented by the Schlafli symbol {3.3.3 2.2 }. It is constructed from 2 faces 21 and 22 of Fig. 1 the top, with 54 2 21 polytopes around every vertex. ...
2 31 polytope
In 7dimensional geometry, 2 31 a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 2 31, describing its branching CoxeterDynkin diagram, with a single ring on the end of a 2nodes. Rectified 2 31 based on the points in the ...
3 21 polytope
In 7dimensional geometry, 3 21 polytope is a uniform 7polytope, constructed within the symmetry e 7 group. It was discovered by Thorold Gosset, published in his paper of 1900. He called it an 7IC semiregular figure. Its Coxeter symbol is 3 21 ...
7cube
In geometry, a 7cube is a sevendimensional hypercube with 128 vertices, edges, 448, 672 square faces, 560 cubic cells, 280 Tesseract 4faces, 84 penteract 5faces, and 14 hexeract 6faces. It can be called the Schlafli symbol {4.3 of 5 }, consi ...
7demicube
In geometry demihepteract or 7demicube is a uniform 7polytope, constructed from the 7hypercube with alternated vertices deleted. It is part of a multidimensional 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 of which re ...
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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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