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2 31 polytope and Coxeter–Dynkin diagram

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

Difference between 2 31 polytope and Coxeter–Dynkin diagram

2 31 polytope vs. Coxeter–Dynkin diagram

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. 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).

Similarities between 2 31 polytope and Coxeter–Dynkin diagram

2 31 polytope and Coxeter–Dynkin diagram have 14 things in common (in Unionpedia): Coxeter element, Coxeter group, E7 (mathematics), Edge (geometry), Face (geometry), Geometry, Harold Scott MacDonald Coxeter, Hyperplane, Projection (linear algebra), Schläfli symbol, Simple Lie group, Tetrahedron, Uniform polytope, Wythoff construction.

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.

2 31 polytope and E7 (mathematics) · Coxeter–Dynkin diagram and E7 (mathematics) · See more »

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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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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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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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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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 such that.

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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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Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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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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Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

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The list above answers the following questions

2 31 polytope and Coxeter–Dynkin diagram Comparison

2 31 polytope has 43 relations, while Coxeter–Dynkin diagram has 117. As they have in common 14, the Jaccard index is 8.75% = 14 / (43 + 117).

References

This article shows the relationship between 2 31 polytope and Coxeter–Dynkin diagram. To access each article from which the information was extracted, please visit:

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