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28 relations: Coxeter group, Coxeter–Dynkin diagram, Facet (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hyperplane, Rectified 8-simplexes, Schläfli symbol, Tetrahedron, Triangle, Uniform 1 k2 polytope, Uniform honeycomb, Vertex figure, Wythoff construction, 1 22 polytope, 1 32 polytope, 1 42 polytope, 16-cell, 2 51 honeycomb, 5 21 honeycomb, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-demicube, 8-demicube.
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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Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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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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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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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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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Triangle
A triangle is a polygon with three edges and three vertices.
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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 honeycomb
In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
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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 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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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-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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5-cell
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
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5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
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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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6-simplex
In geometry, a 6-simplex is a self-dual regular 6-polytope.
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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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Gosset 1 52 honeycomb, Gosset 1 52 lattice.
References
[1] https://en.wikipedia.org/wiki/1_52_honeycomb
