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Uniform polytope and Wythoff construction

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

Difference between Uniform polytope and Wythoff construction

Uniform polytope vs. Wythoff construction

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

Similarities between Uniform polytope and Wythoff construction

Uniform polytope and Wythoff construction have 10 things in common (in Unionpedia): Alternation (geometry), Coxeter–Dynkin diagram, Harold Scott MacDonald Coxeter, Regular polytope, Snub (geometry), Triangular tiling, Uniform 4-polytope, Uniform polyhedron, Uniform tiling, Wythoff symbol.

Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

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Coxeter–Dynkin diagram

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).

Coxeter–Dynkin diagram and Uniform polytope · Coxeter–Dynkin diagram and Wythoff construction · See more »

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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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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Snub (geometry)

In geometry, a snub is an operation applied to a polyhedron.

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Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

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Uniform 4-polytope

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.

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Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

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Uniform tiling

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.

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Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.

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The list above answers the following questions

Uniform polytope and Wythoff construction Comparison

Uniform polytope has 150 relations, while Wythoff construction has 28. As they have in common 10, the Jaccard index is 5.62% = 10 / (150 + 28).

References

This article shows the relationship between Uniform polytope and Wythoff construction. To access each article from which the information was extracted, please visit:

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