- Hexicated 7-simplex
-
7-simplex
Hexicated 7-simplex
Hexitruncated 7-simplex
Hexicantellated 7-simplex
Hexiruncinated 7-simplex
Hexicantitruncated 7-simplex
Hexiruncitruncated 7-simplex
Hexiruncicantellated 7-simplex
Hexisteritruncated 7-simplex
Hexistericantellated 7-simplex
Hexipentitruncated 7-simplex
Hexiruncicantitruncated 7-simplex
Hexistericantitruncated 7-simplex
Hexisteriruncitruncated 7-simplex
Hexisteriruncicantellated 7-simplex
Hexipenticantitruncated 7-simplex
Hexipentiruncitruncated 7-simplex
Hexisteriruncicantitruncated 7-simplex
Hexipentiruncicantitruncated 7-simplex
Hexipentistericantitruncated 7-simplex
Hexipentisteriruncicantitruncated 7-simplex
(Omnitruncated 7-simplex)
Orthogonal projections in A7 Coxeter plane In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex.
There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations.
The simple hexicated 7-simplex is also called an expanded 7-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-simplex. The highest form, the hexipentisteriruncicantitruncated 7-simplex is more simply called a omnitruncated 7-simplex with all of the nodes ringed.
Hexicated 7-simplex
Hexicated 7-simplex Type uniform polyexon Schläfli symbol t0,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 336 Vertices 56 Vertex figure 5-simplex antiprism Coxeter group A7, [[36]], order 80640 Properties convex In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-simplex, or alternately can be seen as an expansion operation.
Root vectors
Its 56 vertices represent the root vectors of the simple Lie group A7.
Alternate names
- Small petated hexadecaexon (acronym: suph) (Jonathan Bowers)[1]
Coordinates
The vertices of the hexicated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,1,1,2). This construction is based on facets of the hexicated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexitruncated 7-simplex
hexitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 1848 Vertices 336 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petitruncated octaexon (acronym: puto) (Jonathan Bowers)[2]
Coordinates
The vertices of the hexitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,1,2,3). This construction is based on facets of the hexitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexicantellated 7-simplex
Hexicantellated 7-simplex Type uniform polyexon Schläfli symbol t0,2,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 5880 Vertices 840 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petirhombated octaexon (acronym: puro) (Jonathan Bowers)[3]
Coordinates
The vertices of the hexicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,2,2,3). This construction is based on facets of the hexicantellated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexiruncinated 7-simplex
Hexiruncinated 7-simplex Type uniform polyexon Schläfli symbol t0,3,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 8400 Vertices 1120 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Petiprismated hexadecaexon (acronym: puph) (Jonathan Bowers)[4]
Coordinates
The vertices of the hexiruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,2,3). This construction is based on facets of the hexiruncinated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexicantitruncated 7-simplex
Hexicantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 8400 Vertices 1680 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petigreatorhombated octaexon (acronym: pugro) (Jonathan Bowers)[5]
Coordinates
The vertices of the hexicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,2,3,4). This construction is based on facets of the hexicantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexiruncitruncated 7-simplex
Hexiruncitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,3,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 20160 Vertices 3360 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petiprismatotruncated octaexon (acronym: pupato) (Jonathan Bowers)[6]
Coordinates
The vertices of the hexiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,2,2,3,4). This construction is based on facets of the hexiruncitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexiruncicantellated 7-simplex
Hexiruncicantellated 7-simplex Type uniform polyexon Schläfli symbol t0,2,3,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 16800 Vertices 3360 Vertex figure Coxeter group A7, [36], order 40320 Properties convex In seven-dimensional geometry, a hexiruncicantellated 7-simplex is a uniform 7-polytope.
Alternate names
- Petiprismatorhombated octaexon (acronym: pupro) (Jonathan Bowers)[7]
Coordinates
The vertices of the hexiruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,2,3,3,4). This construction is based on facets of the hexiruncicantellated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexisteritruncated 7-simplex
hexisteritruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,4,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 20160 Vertices 3360 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Peticellitruncated octaexon (acronym: pucto) (Jonathan Bowers)[8]
Coordinates
The vertices of the hexisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,2,3,4). This construction is based on facets of the hexisteritruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexistericantellated 7-simplex
hexistericantellated 7-simplex Type uniform polyexon Schläfli symbol t0,2,4,6{36} Coxeter-Dynkin diagrams 6-faces t0,2,4{3,3,3,3,3}
{}xt0,2,4{3,3,3,3}
{3}xt0,2{3,3,3}
t0,2{3,3}xt0,2{3,3}5-faces 4-faces Cells Faces Edges 30240 Vertices 5040 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Peticellirhombihexadecaexon (acronym: pucroh) (Jonathan Bowers)[9]
Coordinates
The vertices of the hexistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,3,4). This construction is based on facets of the hexistericantellated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexipentitruncated 7-simplex
Hexipentitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 8400 Vertices 1680 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Petiteritruncated hexadecaexon (acronym: putath) (Jonathan Bowers)[10]
Coordinates
The vertices of the hexipentitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,2,2,3,4). This construction is based on facets of the hexipentitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexiruncicantitruncated 7-simplex
Hexiruncicantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,3,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 30240 Vertices 6720 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petigreatoprismated octaexon (acronym: pugopo) (Jonathan Bowers)[11]
Coordinates
The vertices of the hexiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,4,5). This construction is based on facets of the hexiruncicantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexistericantitruncated 7-simplex
Hexistericantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,4,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 50400 Vertices 10080 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Peticelligreatorhombated octaexon (acronym: pucagro) (Jonathan Bowers)[12]
Coordinates
The vertices of the hexistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,4,5). This construction is based on facets of the hexistericantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexisteriruncitruncated 7-simplex
Hexisteriruncitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,3,4,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 45360 Vertices 10080 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Peticelliprismatotruncated octaexon (acronym: pucpato) (Jonathan Bowers)[13]
Coordinates
The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,3,4,5). This construction is based on facets of the hexisteriruncitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexisteriruncicantellated 7-simplex
Hexisteriruncitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,2,3,4,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 45360 Vertices 10080 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Peticelliprismatorhombihexadecaexon (acronym: pucproh) (Jonathan Bowers)[14]
Coordinates
The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,4,5). This construction is based on facets of the hexisteriruncitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexipenticantitruncated 7-simplex
hexipenticantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 30240 Vertices 6720 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petiterigreatorhombated octaexon (acronym: putagro) (Jonathan Bowers)[15]
Coordinates
The vertices of the hexipenticantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,2,3,4,5). This construction is based on facets of the hexipenticantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [7] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [5] [4] [3] Hexipentiruncitruncated 7-simplex
Hexisteriruncicantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,3,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 80640 Vertices 20160 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Petiteriprismatotruncated hexadecaexon (acronym: putpath) (Jonathan Bowers)[16]
Coordinates
The vertices of the hexisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,5,6). This construction is based on facets of the hexisteriruncicantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexisteriruncicantitruncated 7-simplex
Hexisteriruncicantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,3,4,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 80640 Vertices 20160 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petigreatocellated octaexon (acronym: pugaco) (Jonathan Bowers)[17]
Coordinates
The vertices of the hexisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,5,6). This construction is based on facets of the hexisteriruncicantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph Dihedral symmetry [[5]] [4] [[3]] Hexipentiruncicantitruncated 7-simplex
Hexipentiruncicantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,3,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 80640 Vertices 20160 Vertex figure Coxeter group A7, [36], order 40320 Properties convex Alternate names
- Petiterigreatoprismated octaexon (acronym: putgapo) (Jonathan Bowers)[18]
Coordinates
The vertices of the hexipentiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,3,4,5,6). This construction is based on facets of the hexipentiruncicantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Hexipentistericantitruncated 7-simplex
Hexipentistericantitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,4,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 80640 Vertices 20160 Vertex figure Coxeter group A7, [[36]], order 80640 Properties convex Alternate names
- Petitericelligreatorhombihexadecaexon (acronym: putcagroh) (Jonathan Bowers)[19]
Coordinates
The vertices of the hexipentistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,3,3,4,5,6). This construction is based on facets of the hexipentistericantitruncated 8-orthoplex.
Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Omnitruncated 7-simplex
Omnitruncated 7-simplex Type uniform polyexon Schläfli symbol t0,1,2,3,4,5,6{36} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 141120 Vertices 40320 Vertex figure Irr. 6-simplex Coxeter group A7, [[36]], order 80640 Properties convex The omnitruncated 7-simplex is composed of 40320 (8 factorial) vertices and is the largest uniform 7-polytope in the A7 symmetry of the regular 7-simplex. It can also be called the hexipentisteriruncicantitruncated 7-simplex which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.
The omnitruncated 7-simplex is the permutohedron of order 8. The omnitruncated 7-simplex is a zonotope, the Minkowski sum of eight line segments parallel to the eight lines through the origin and the eight vertices of the 7-simplex.
Like all uniform omnitruncated n-simplices, the omnitruncated 7-simplex can tessellate space by itself, in this case 7-dimensional space with three facets around each ridge. It has Coxeter-Dynkin diagram of
.Alternate names
- Great petated hexadecaexon (Acronym: guph) (Jonathan Bowers)[20]
Coordinates
The vertices of the omnitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,3,4,5,6,7). This construction is based on facets of the hexipentisteriruncicantitruncated 8-orthoplex, t0,1,2,3,4,5,6{36,4},
.Images
orthographic projections Ak Coxeter plane A7 A6 A5 Graph 
Dihedral symmetry [8] [[7]] [6] Ak Coxeter plane A4 A3 A2 Graph 
Dihedral symmetry [[5]] [4] [[3]] Related polytopes
These polytope are a part of 71 uniform 7-polytopes with A7 symmetry.
Notes
- ^ Klitizing, (x3o3o3o3o3o3x - suph)
- ^ Klitizing, (x3x3o3o3o3o3x- puto)
- ^ Klitizing, (x3o3x3o3o3o3x - puro)
- ^ Klitizing, (x3o3o3x3o3o3x - puph)
- ^ Klitizing, (x3o3o3o3x3o3x - pugro)
- ^ Klitizing, (x3x3x3o3o3o3x - pupato)
- ^ Klitizing, (x3o3x3x3o3o3x - pupro)
- ^ Klitizing, (x3x3o3o3x3o3x - pucto)
- ^ Klitizing, (x3o3x3o3x3o3x - pucroh)
- ^ Klitizing, (x3x3o3o3o3x3x - putath)
- ^ Klitizing, (x3x3x3x3o3o3x - pugopo)
- ^ Klitizing, (x3x3x3o3x3o3x - pucagro)
- ^ Klitizing, (x3x3o3x3x3o3x - pucpato)
- ^ Klitizing, (x3o3x3x3x3o3x - pucproh)
- ^ Klitizing, (x3x3x3o3o3x3x - putagro)
- ^ Klitizing, (x3x3x3x3o3x3x - putpath)
- ^ Klitizing, (x3x3x3x3x3o3x - pugaco)
- ^ Klitzing, (x3x3x3x3o3x3x - putgapo)
- ^ Klitizing, (x3x3x3o3x3x3x - putcagroh)
- ^ Klitizing, (x3x3x3x3x3x3x - guph)
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6, wiley.com
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD (1966)
- Richard Klitzing, , 7D x3o3o3o3o3o3x - suph, x3x3o3o3o3o3x- puto, x3o3x3o3o3o3x - puro, x3o3o3x3o3o3x - puph, x3o3o3o3x3o3x - pugro, x3x3x3o3o3o3x - pupato, x3o3x3x3o3o3x - pupro, x3x3o3o3x3o3x - pucto, x3o3x3o3x3o3x - pucroh, x3x3o3o3o3x3x - putath, x3x3x3x3o3o3x - pugopo, x3x3x3o3x3o3x - pucagro, x3x3o3x3x3o3x - pucpato, x3o3x3x3x3o3x - pucproh, x3x3x3o3o3x3x - putagro, x3x3x3x3o3x3x - putpath, x3x3x3x3x3o3x - pugaco, x3x3x3x3o3x3x - putgapo, x3x3x3o3x3x3x - putcagroh, x3x3x3x3x3x3x - guph
External links
- Olshevsky, George, Cross polytope at Glossary for Hyperspace.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
Fundamental convex regular and uniform polytopes in dimensions 2–10 Family An BCn Dn E6 / E7 / E8 / F4 / G2 Hn Regular polygon Triangle Square Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform polychoron 5-cell 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221 Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321 Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421 Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube n-polytopes n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 pentagonal polytope Topics: Polytope families • Regular polytope • List of regular polytopes Categories:- 7-polytopes
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