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Steric 7-cubes

Index Steric 7-cubes

In seven-dimensional geometry, a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube. [1]

Table of Contents

  1. 18 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Demihypercube, Geometry, Harold Scott MacDonald Coxeter, Hypercube, Norman Johnson (mathematician), Projection (linear algebra), Runcination, Schläfli symbol, Uniform 7-polytope, Uniform polytope, Vertex figure, 7-demicube.

  2. 7-polytopes

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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Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

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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.

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Coxeter element

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

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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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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.

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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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Geometry

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

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Harold Scott MacDonald Coxeter

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

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Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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Norman Johnson (mathematician)

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

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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.

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Runcination

In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges, and vertices, creating new facets in place of the original face, edge, and vertex centers.

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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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Uniform 7-polytope

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

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Uniform polytope

In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform 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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7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. Steric 7-cubes and 7-demicube are 7-polytopes.

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See also

7-polytopes

References

[1] https://en.wikipedia.org/wiki/Steric_7-cubes

Also known as Runcinated 7-demicube, Runcinated 7-demicubes, Steric 7-cube, Stericantellated 7-demicube, Stericantic 7-cube, Stericated 7-demicube, Stericated 7-demicubes, Steriruncic 7-cube, Steriruncicantic 7-cube, Steritruncated 7-demicube.