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10-orthoplex and Gosset–Elte figures

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

Difference between 10-orthoplex and Gosset–Elte figures

10-orthoplex vs. Gosset–Elte figures

In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5-cells 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces. 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.

Similarities between 10-orthoplex and Gosset–Elte figures

10-orthoplex and Gosset–Elte figures have 18 things in common (in Unionpedia): Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Petrie polygon, Projection (linear algebra), Regular polytope, Tetrahedron, Vertex figure, 5-cell, 5-simplex, 6-simplex, 7-simplex, 8-simplex, 9-orthoplex, 9-simplex.

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).

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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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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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Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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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.

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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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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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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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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.

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6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope.

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7-simplex

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.

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8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope.

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9-orthoplex

In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.

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9-simplex

In geometry, a 9-simplex is a self-dual regular 9-polytope.

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The list above answers the following questions

10-orthoplex and Gosset–Elte figures Comparison

10-orthoplex has 33 relations, while Gosset–Elte figures has 77. As they have in common 18, the Jaccard index is 16.36% = 18 / (33 + 77).

References

This article shows the relationship between 10-orthoplex and Gosset–Elte figures. To access each article from which the information was extracted, please visit:

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