6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope

6faces 14 4,34 5faces 84 4,33 4faces 280 4,3,3 Cells 560 4,3 Faces 672 4 Edges 448 Vertices 128 Vertex figure
6simplex
Petrie polygon tetradecagon Coxeter group C7, [35,4] Dual 7orthoplex Properties convex In geometry, a
7cube
Contents 1 Related polytopes 2 As a configuration 3 Cartesian coordinates 4 Images 5 References 6 External links Related polytopes[edit]
It is a part of an infinite family of polytopes, called hypercubes.
The dual of a
7cube
[ 128 7 21 35 35 21 7 2 448 6 15 20 15 6 4 4 672 5 10 10 5 8 12 6 560 4 6 4 16 32 24 8 280 3 3 32 80 80 40 10 84 2 64 192 240 160 60 12 14 ] displaystyle begin bmatrix begin matrix 128&7&21&35&35&21&7\2&448&6&15&20&15&6\4&4&672&5&10&10&5\8&12&6&560&4&6&4\16&32&24&8&280&3&3\32&80&80&40&10&84&2\64&192&240&160&60&12&14end matrix end bmatrix Cartesian coordinates[edit]
Cartesian coordinates
(±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6) with 1 < xi < 1. Images[edit] This hypercube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertexedgevertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1. Play media Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D. orthographic projections Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4 Graph Dihedral symmetry [14] [12] [10] Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3 Graph Dihedral symmetry [8] [6] [4] Coxeter plane A5 A3 Graph Dihedral symmetry [6] [4] References[edit] ^ Coxeter, Regular Polytopes, sec 1.8 Configurations ^ Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n≥5) Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and SemiRegular Polytopes II, [Math. Zeit. 188 (1985) 559591] (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345] Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "7D uniform polytopes (polyexa) o3o3o3o3o3o4x  hept". External links[edit] Weisstein, Eric W. "Hypercube". MathWorld.
Weisstein, Eric W. "
Hypercube
v t e Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square pgon Hexagon Pentagon Uniform polyhedron
Tetrahedron
Octahedron
Dodecahedron • Icosahedron Uniform 4polytope
5cell
16cell
Uniform 5polytope
5simplex
5orthoplex
Uniform 6polytope
6simplex
6orthoplex
Uniform 7polytope
7simplex
7orthoplex
Uniform 8polytope
8simplex
8orthoplex
Uniform 9polytope
9simplex
9orthoplex
Uniform 10polytope
10simplex
10orthoplex
Uniform npolytope nsimplex northoplex • ncube ndemicube 1k2 • 2k1 • k21 npentagonal polytope Topics:
Polytope
