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57 relations: A6 polytope, Cantellated 6-simplexes, Complex polytope, Coxeter group, Cyclotruncated 6-simplex honeycomb, Cyclotruncated simplectic honeycomb, E9 honeycomb, Emanuel Lodewijk Elte, Gosset–Elte figures, Heptagon, Hexicated 7-simplexes, List of mathematical shapes, List of polygons, polyhedra and polytopes, List of regular polytopes and compounds, Omnitruncated 6-simplex honeycomb, Omnitruncated simplectic honeycomb, Pentellated 6-simplexes, Point group, Polytope families, Rectified 6-simplexes, Runcinated 6-simplexes, Simplectic honeycomb, Simplex, Six-dimensional space, Stericated 6-simplexes, Truncated 6-simplexes, Truncated 7-simplexes, Uniform 2 k1 polytope, Uniform 6-polytope, Uniform k 21 polytope, 1 42 polytope, 1 52 honeycomb, 10-demicube, 10-orthoplex, 10-simplex, 2 31 polytope, 2 41 polytope, 2 51 honeycomb, 3 21 polytope, 3 31 honeycomb, 4 21 polytope, 5 21 honeycomb, 6-polytope, 6-simplex honeycomb, 7-cube, 7-demicube, 7-orthoplex, 7-simplex, 7-simplex honeycomb, 8-cube, ..., 8-demicube, 8-orthoplex, 8-simplex, 8-simplex honeycomb, 9-demicube, 9-orthoplex, 9-simplex. Expand index (7 more) »
A6 polytope
In 6-dimensional geometry, there are 35 uniform polytopes with A6 symmetry.
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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.
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Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.
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Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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Cyclotruncated 6-simplex honeycomb
In six-dimensional Euclidean geometry, the cyclotruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb).
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Cyclotruncated simplectic honeycomb
In geometry, the cyclotruncated simplectic honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the _n affine Coxeter group.
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E9 honeycomb
In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space.
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Emanuel Lodewijk Elte
Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.
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Gosset–Elte figures
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.
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Heptagon
In geometry, a heptagon is a seven-sided polygon or 7-gon.
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Hexicated 7-simplexes
In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex.
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List of mathematical shapes
Following is a list of some mathematically well-defined shapes.
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List of polygons, polyhedra and polytopes
A polytope is a geometric object with flat sides, which exists in any general number of dimensions.
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List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
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Omnitruncated 6-simplex honeycomb
In six-dimensional Euclidean geometry, the omnitruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb).
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Omnitruncated simplectic honeycomb
In geometry an omnitruncated simplectic honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry of the _n affine Coxeter group.
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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.
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Point group
In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed.
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Polytope families
There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality.
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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.
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Runcinated 6-simplexes
In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex.
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Simplectic honeycomb
In geometry, the simplectic honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the _n affine Coxeter group symmetry.
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Six-dimensional space
Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space.
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Stericated 6-simplexes
In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex.
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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.
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Truncated 7-simplexes
In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.
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Uniform 2 k1 polytope
In geometry, 2k1 polytope is a uniform polytope in n dimensions (n.
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Uniform 6-polytope
In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.
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Uniform k 21 polytope
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.
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1 42 polytope
In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group.
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1 52 honeycomb
In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space.
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10-demicube
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed.
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10-orthoplex
In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5-cells 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces.
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10-simplex
In geometry, a 10-simplex is a self-dual regular 10-polytope.
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2 31 polytope
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
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2 41 polytope
In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group.
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2 51 honeycomb
In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation.
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3 21 polytope
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group.
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3 31 honeycomb
In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.
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4 21 polytope
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.
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5 21 honeycomb
In geometry, the 521 honeycomb is a uniform tessellation of 8-dimensional Euclidean space.
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6-polytope
In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets.
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6-simplex honeycomb
In six-dimensional Euclidean geometry, the 6-simplex honeycomb is a space-filling tessellation (or honeycomb).
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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.
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7-demicube
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed.
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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.
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7-simplex
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.
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7-simplex honeycomb
In seven-dimensional Euclidean geometry, the 7-simplex honeycomb is a space-filling tessellation (or honeycomb).
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8-cube
In geometry, an 8-cube is an eight-dimensional hypercube (8-cube).
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8-demicube
In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed.
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8-orthoplex
In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.
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8-simplex
In geometry, an 8-simplex is a self-dual regular 8-polytope.
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8-simplex honeycomb
In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb).
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9-demicube
In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed.
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9-orthoplex
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.
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9-simplex
In geometry, a 9-simplex is a self-dual regular 9-polytope.
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References
[1] https://en.wikipedia.org/wiki/6-simplex
