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48 relations: Alternation (geometry), B5 polytope, Cantic 5-cube, Coxeter element, Coxeter group, D5 polytope, Demihypercube, E5, E9 honeycomb, Emanuel Lodewijk Elte, Five-dimensional space, Gosset–Elte figures, Halved cube graph, Hyperoctahedral group, List of mathematical shapes, List of polygons, polyhedra and polytopes, Octagon, Point group, Polytope families, Quarter 5-cubic honeycomb, Quarter hypercubic honeycomb, Rectified 5-cell, Runcic 5-cubes, Semiregular polytope, Steric 5-cubes, Uniform 1 k2 polytope, Uniform 5-polytope, Uniform 6-polytope, Uniform k 21 polytope, 1 22 polytope, 1 32 polytope, 1 33 honeycomb, 1 42 polytope, 1 52 honeycomb, 10-demicube, 2 21 polytope, 3 21 polytope, 4 21 polytope, 5 21 honeycomb, 5-cube, 5-cubic honeycomb, 5-demicubic honeycomb, 5-polytope, 6-cube, 6-demicube, 7-demicube, 8-demicube, 9-demicube.
Alternation (geometry)
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
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B5 polytope
In 5-dimensional geometry, there are 31 uniform polytopes with B5 symmetry.
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Cantic 5-cube
In geometry of five dimensions or higher, a cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube.
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Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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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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D5 polytope
In 5-dimensional geometry, there are 23 uniform polytopes with D5 symmetry, 8 are unique, and 15 are shared with the B5 symmetry.
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Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.
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E5
E5, E05 or E-5 may refer to.
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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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Five-dimensional space
A five-dimensional space is a space with five dimensions.
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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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Halved cube graph
In graph theory, the halved cube graph or half cube graph of order n is the graph of the demihypercube, formed by connecting pairs of vertices at distance exactly two from each other in the hypercube graph.
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Hyperoctahedral group
In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope.
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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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Octagon
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
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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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Quarter 5-cubic honeycomb
In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb).
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Quarter hypercubic honeycomb
In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb.
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Rectified 5-cell
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.
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Runcic 5-cubes
In six-dimensional geometry, a runcic 5-cube or (runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope.
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Semiregular polytope
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.
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Steric 5-cubes
In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope.
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Uniform 1 k2 polytope
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
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Uniform 5-polytope
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
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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 22 polytope
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
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1 32 polytope
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.
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1 33 honeycomb
In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol, and is composed of 132''' 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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2 21 polytope
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
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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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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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5-cube
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
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5-cubic honeycomb
The 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space.
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5-demicubic honeycomb
The 5-demicube honeycomb, or demipenteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space.
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5-polytope
In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.
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6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
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6-demicube
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
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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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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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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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1 21 polytope, 5-demihypercube, Demipenteract, E5 polytope, Gosset 1 12 polytope, Gosset 1 21 polytope, Half 5-cube, Hemipenteract.
References
[1] https://en.wikipedia.org/wiki/5-demicube
