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Uniform 5-polytope and Uniform polyhedron

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

Difference between Uniform 5-polytope and Uniform polyhedron

Uniform 5-polytope vs. Uniform polyhedron

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. 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).

Similarities between Uniform 5-polytope and Uniform polyhedron

Uniform 5-polytope and Uniform polyhedron have 22 things in common (in Unionpedia): Alternation (geometry), Cantellation (geometry), Coxeter group, Coxeter–Dynkin diagram, Dual polyhedron, Expansion (geometry), Face (geometry), Harold Scott MacDonald Coxeter, Isogonal figure, Norman Johnson (mathematician), Pentagonal antiprism, Pentagonal prism, Prism (geometry), Rectification (geometry), Regular polygon, Schläfli symbol, Tetrahedron, Triangular prism, Truncation (geometry), Uniform polytope, Vertex figure, Wythoff construction.

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.

Alternation (geometry) and Uniform 5-polytope · Alternation (geometry) and Uniform polyhedron · See more »

Cantellation (geometry)

In geometry, a cantellation is an operation in any dimension that bevels a regular polytope at its edges and vertices, creating a new facet in place of each edge and vertex.

Cantellation (geometry) and Uniform 5-polytope · Cantellation (geometry) and Uniform polyhedron · 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).

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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 5-polytope · Coxeter–Dynkin diagram and Uniform polyhedron · See more »

Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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Expansion (geometry)

In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.

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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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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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Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

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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.

Norman Johnson (mathematician) and Uniform 5-polytope · Norman Johnson (mathematician) and Uniform polyhedron · See more »

Pentagonal antiprism

In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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Pentagonal prism

In geometry, the pentagonal prism is a prism with a pentagonal base.

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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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Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

Rectification (geometry) and Uniform 5-polytope · Rectification (geometry) and Uniform polyhedron · See more »

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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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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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.

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Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

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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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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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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

Uniform 5-polytope and Uniform polyhedron Comparison

Uniform 5-polytope has 118 relations, while Uniform polyhedron has 127. As they have in common 22, the Jaccard index is 8.98% = 22 / (118 + 127).

References

This article shows the relationship between Uniform 5-polytope and Uniform polyhedron. To access each article from which the information was extracted, please visit:

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