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Coxeter–Dynkin diagram and Uniform 8-polytope

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Coxeter–Dynkin diagram and Uniform 8-polytope

Coxeter–Dynkin diagram vs. Uniform 8-polytope

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes). In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.

Similarities between Coxeter–Dynkin diagram and Uniform 8-polytope

Coxeter–Dynkin diagram and Uniform 8-polytope have 14 things in common (in Unionpedia): Coxeter element, Coxeter group, E7 (mathematics), E8 (mathematics), Face (geometry), Facet (geometry), Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Polytope, Prism (geometry), Schläfli symbol, Simplex, Uniform polytope.

Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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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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E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.

Coxeter–Dynkin diagram and E7 (mathematics) · E7 (mathematics) and Uniform 8-polytope · See more »

E8 (mathematics)

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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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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Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

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The list above answers the following questions

Coxeter–Dynkin diagram and Uniform 8-polytope Comparison

Coxeter–Dynkin diagram has 117 relations, while Uniform 8-polytope has 61. As they have in common 14, the Jaccard index is 7.87% = 14 / (117 + 61).

References

This article shows the relationship between Coxeter–Dynkin diagram and Uniform 8-polytope. To access each article from which the information was extracted, please visit:

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