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2 21 polytope and Coxeter–Dynkin diagram

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

Difference between 2 21 polytope and Coxeter–Dynkin diagram

2 21 polytope vs. Coxeter–Dynkin diagram

In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 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 21 polytope and Coxeter–Dynkin diagram

2 21 polytope and Coxeter–Dynkin diagram have 16 things in common (in Unionpedia): Complex polytope, Complex reflection group, Coxeter element, Coxeter group, Dynkin diagram, E6 (mathematics), Geometry, Harold Scott MacDonald Coxeter, Ludwig Schläfli, Projection (linear algebra), Regular polytope, Schläfli symbol, Simplex, Tetrahedron, Triangular prism, Uniform polytope.

Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

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Complex reflection group

In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.

2 21 polytope and Complex reflection group · Complex reflection group and Coxeter–Dynkin diagram · See more »

Coxeter element

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

2 21 polytope and Coxeter element · Coxeter element and Coxeter–Dynkin diagram · See more »

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).

2 21 polytope and Coxeter group · Coxeter group and Coxeter–Dynkin diagram · See more »

Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).

2 21 polytope and Dynkin diagram · Coxeter–Dynkin diagram and Dynkin diagram · See more »

E6 (mathematics)

In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.

2 21 polytope and E6 (mathematics) · Coxeter–Dynkin diagram and E6 (mathematics) · See more »

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.

2 21 polytope and Harold Scott MacDonald Coxeter · Coxeter–Dynkin diagram and Harold Scott MacDonald Coxeter · See more »

Ludwig Schläfli

Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.

2 21 polytope and Ludwig Schläfli · Coxeter–Dynkin diagram and Ludwig Schläfli · See more »

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

2 21 polytope and Projection (linear algebra) · Coxeter–Dynkin diagram and Projection (linear algebra) · See more »

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

2 21 polytope and Schläfli symbol · Coxeter–Dynkin diagram and Schläfli symbol · See more »

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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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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Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

2 21 polytope and Triangular prism · Coxeter–Dynkin diagram and Triangular prism · See more »

Uniform polytope

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

2 21 polytope and Uniform polytope · Coxeter–Dynkin diagram and Uniform polytope · See more »

The list above answers the following questions

2 21 polytope and Coxeter–Dynkin diagram Comparison

2 21 polytope has 49 relations, while Coxeter–Dynkin diagram has 117. As they have in common 16, the Jaccard index is 9.64% = 16 / (49 + 117).

References

This article shows the relationship between 2 21 polytope and Coxeter–Dynkin diagram. To access each article from which the information was extracted, please visit:

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