Coxeter group and Rectified 5-simplexes

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Difference between Coxeter group and Rectified 5-simplexes

Coxeter group vs. Rectified 5-simplexes

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). In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.

Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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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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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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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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Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform 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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2 22 honeycomb

In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.

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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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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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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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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-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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