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41 relations: A8 polytope, Cantellated 8-simplexes, Coxeter group, Cyclotruncated 8-simplex honeycomb, Cyclotruncated simplectic honeycomb, E8 lattice, E9 honeycomb, Eight-dimensional space, Emanuel Lodewijk Elte, Gosset–Elte figures, Heptellated 8-simplexes, Hexicated 8-simplexes, List of mathematical shapes, List of polygons, polyhedra and polytopes, List of regular polytopes and compounds, Nonagon, Omnitruncated 8-simplex honeycomb, Omnitruncated simplectic honeycomb, Pentellated 8-simplexes, Point group, Polytope families, Rectified 8-simplexes, Runcinated 8-simplexes, Simplectic honeycomb, Simplex, Stericated 8-simplexes, Truncated 8-simplexes, Uniform 2 k1 polytope, Uniform 8-polytope, Uniform k 21 polytope, 10-demicube, 10-orthoplex, 10-simplex, 2 51 honeycomb, 5 21 honeycomb, 8-orthoplex, 8-simplex honeycomb, 9-cube, 9-demicube, 9-orthoplex, 9-simplex.
A8 polytope
In 8-dimensional geometry, there are 135 uniform polytopes with A8 symmetry.
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Cantellated 8-simplexes
In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.
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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 8-simplex honeycomb
In eight-dimensional Euclidean geometry, the cyclotruncated 8-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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E8 lattice
In mathematics, the E8 lattice is a special lattice in R8.
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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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Eight-dimensional space
In mathematics, a sequence of n real numbers can be understood as a location in n-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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Heptellated 8-simplexes
In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex.
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Hexicated 8-simplexes
In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-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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Nonagon
In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.
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Omnitruncated 8-simplex honeycomb
In eight-dimensional Euclidean geometry, the omnitruncated 8-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 8-simplexes
In eight-dimensional geometry, a pentellated 8-simplex is a convex uniform 8-polytope with 5th order truncations of the regular 8-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 8-simplexes
In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex.
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Runcinated 8-simplexes
In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-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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Stericated 8-simplexes
In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex.
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Truncated 8-simplexes
In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-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 8-polytope
In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.
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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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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 51 honeycomb
In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation.
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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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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 honeycomb
In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb).
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9-cube
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.
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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/8-simplex
