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3 21 polytope and 6-orthoplex

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

Difference between 3 21 polytope and 6-orthoplex

3 21 polytope vs. 6-orthoplex

In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.

Similarities between 3 21 polytope and 6-orthoplex

3 21 polytope and 6-orthoplex have 20 things in common (in Unionpedia): Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hosohedron, Petrie polygon, Projection (linear algebra), Regular polytope, Schläfli symbol, Tetrahedron, Triangle, Uniform 6-polytope, Vertex figure, 5-cell, 5-simplex.

Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

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Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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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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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).

3 21 polytope and Coxeter–Dynkin diagram · 6-orthoplex and Coxeter–Dynkin diagram · See more »

Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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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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Gosset–Elte figures

In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.

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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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Hosohedron

In geometry, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

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Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.

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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.

3 21 polytope and Projection (linear algebra) · 6-orthoplex 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.

3 21 polytope and Regular polytope · 6-orthoplex and Regular polytope · See more »

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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Triangle

A triangle is a polygon with three edges and three vertices.

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Uniform 6-polytope

In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.

3 21 polytope and Uniform 6-polytope · 6-orthoplex and Uniform 6-polytope · See more »

Vertex figure

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

3 21 polytope and Vertex figure · 6-orthoplex and Vertex figure · See more »

5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

3 21 polytope and 5-simplex · 5-simplex and 6-orthoplex · See more »

The list above answers the following questions

3 21 polytope and 6-orthoplex Comparison

3 21 polytope has 48 relations, while 6-orthoplex has 38. As they have in common 20, the Jaccard index is 23.26% = 20 / (48 + 38).

References

This article shows the relationship between 3 21 polytope and 6-orthoplex. To access each article from which the information was extracted, please visit:

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