D7 polytope

In 7-dimensional geometry, there are 95 uniform polytopes with D7 symmetry; 32 are unique, and 63 are shared with the B7 symmetry. ^[1]

14 relations: Cantic 7-cube, Coxeter element, Coxeter–Dynkin diagram, Geometry, Harold Scott MacDonald Coxeter, Hexic 7-cubes, Norman Johnson (mathematician), Orthographic projection, Pentic 7-cubes, Runcic 7-cubes, Steric 7-cubes, Uniform 7-polytope, 7-demicube, 7-orthoplex.
7-polytopes

Cantic 7-cube

In seven-dimensional geometry, a cantic 7-cube or truncated 7-demicube as a uniform 7-polytope, being a truncation of the 7-demicube. D7 polytope and cantic 7-cube are 7-polytopes.

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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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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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Hexic 7-cubes

In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. D7 polytope and hexic 7-cubes are 7-polytopes.

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Norman Johnson (mathematician)

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

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Orthographic projection

Orthographic projection (also orthogonal projection and analemma) is a means of representing three-dimensional objects in two dimensions.

See D7 polytope and Orthographic projection

Pentic 7-cubes

In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. D7 polytope and pentic 7-cubes are 7-polytopes.

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Runcic 7-cubes

In seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. D7 polytope and runcic 7-cubes are 7-polytopes.

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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. D7 polytope and steric 7-cubes are 7-polytopes.

See D7 polytope and Steric 7-cubes

Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. D7 polytope and Uniform 7-polytope are 7-polytopes.

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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. D7 polytope and 7-demicube are 7-polytopes.

See D7 polytope and 7-demicube

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. D7 polytope and 7-orthoplex are 7-polytopes.

See D7 polytope and 7-orthoplex

References

[1] https://en.wikipedia.org/wiki/D7_polytope

Also known as List of D7 polytopes.

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