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Cantellated 7-cubes

Index Cantellated 7-cubes

In seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube. [1]

Table of Contents

  1. 17 relations: B7 polytope, Cantellated 7-orthoplexes, Cantellation (geometry), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Projection (linear algebra), Rectified 7-cubes, Schläfli symbol, Uniform 7-polytope, Vertex figure, 7-cube, 7-orthoplex.

  2. 7-polytopes

B7 polytope

In 7-dimensional geometry, there are 128 uniform polytopes with B7 symmetry. Cantellated 7-cubes and B7 polytope are 7-polytopes.

See Cantellated 7-cubes and B7 polytope

Cantellated 7-orthoplexes

In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex. Cantellated 7-cubes and cantellated 7-orthoplexes are 7-polytopes.

See Cantellated 7-cubes and Cantellated 7-orthoplexes

Cantellation (geometry)

In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex.

See Cantellated 7-cubes and Cantellation (geometry)

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n.

See Cantellated 7-cubes and Convex polytope

Coxeter element

In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections.

See Cantellated 7-cubes and Coxeter element

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).

See Cantellated 7-cubes and Coxeter group

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

See Cantellated 7-cubes and Coxeter–Dynkin diagram

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Cantellated 7-cubes and Geometry

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

See Cantellated 7-cubes and Harold Scott MacDonald Coxeter

Norman Johnson (mathematician)

Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.

See Cantellated 7-cubes and Norman Johnson (mathematician)

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.

See Cantellated 7-cubes and Projection (linear algebra)

Rectified 7-cubes

In seven-dimensional geometry, a rectified 7-cube is a convex uniform 7-polytope, being a rectification of the regular 7-cube. Cantellated 7-cubes and rectified 7-cubes are 7-polytopes.

See Cantellated 7-cubes and Rectified 7-cubes

Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.

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Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Cantellated 7-cubes and Uniform 7-polytope are 7-polytopes.

See Cantellated 7-cubes and Uniform 7-polytope

Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

See Cantellated 7-cubes and Vertex figure

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. Cantellated 7-cubes and 7-cube are 7-polytopes.

See Cantellated 7-cubes and 7-cube

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. Cantellated 7-cubes and 7-orthoplex are 7-polytopes.

See Cantellated 7-cubes and 7-orthoplex

See also

7-polytopes

References

[1] https://en.wikipedia.org/wiki/Cantellated_7-cubes

Also known as Bicantellated 7-cube, Bicantitruncated 7-cube, Cantellated 7-cube, Cantitruncated 7-cube, Tricantellated 7-cube, Tricantitruncated 7-cube, Trirhombihepteractihecatonicosoctaexon.