Runcinated 7-orthoplexes

In seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex. ^[1]

15 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Projection (linear algebra), Runcination, Schläfli symbol, Truncation (geometry), Uniform 7-polytope, Vertex figure, 7-cube, 7-orthoplex.
7-polytopes

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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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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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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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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Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

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Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Runcinated 7-orthoplexes 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. Runcinated 7-orthoplexes 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. Runcinated 7-orthoplexes and 7-orthoplex are 7-polytopes.

See Runcinated 7-orthoplexes and 7-orthoplex

References

[1] https://en.wikipedia.org/wiki/Runcinated_7-orthoplexes

Also known as Biruncicantellated 7-orthoplex, Biruncicantitruncated 7-orthoplex, Biruncinated 7-orthoplex, Biruncitruncated 7-orthoplex, Runcicantellated 7-orthoplex, Runcicantitruncated 7-orthoplex, Runcinated 7-orthoplex, Runcitruncated 7-orthoplex.

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