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Rectified 7-cubes

Index 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. [1]

Table of Contents

  1. 18 relations: Cartesian coordinate system, Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cube, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Projection (linear algebra), Rectification (geometry), Rectified 7-orthoplexes, Schläfli symbol, Uniform 7-polytope, Vertex figure, 7-cube, 7-orthoplex.

  2. 7-polytopes

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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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces.

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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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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 (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

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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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Rectification (geometry)

In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

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Rectified 7-orthoplexes

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

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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. Rectified 7-cubes and Uniform 7-polytope are 7-polytopes.

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

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

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See also

7-polytopes

References

[1] https://en.wikipedia.org/wiki/Rectified_7-cubes

Also known as Birectified 7-cube, Rectified 7-cube, Rectified demihepteract, Trirectified 7-cube.