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5 21 honeycomb and 8-orthoplex

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

Difference between 5 21 honeycomb and 8-orthoplex

5 21 honeycomb vs. 8-orthoplex

In geometry, the 521 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.

Similarities between 5 21 honeycomb and 8-orthoplex

5 21 honeycomb and 8-orthoplex have 19 things in common (in Unionpedia): Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Face (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Regular polytope, Schläfli symbol, Tetrahedron, Triangle, Vertex figure, Wythoff construction, 5-cell, 5-simplex, 6-simplex, 7-simplex, 8-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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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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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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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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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.

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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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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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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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The list above answers the following questions

5 21 honeycomb and 8-orthoplex Comparison

5 21 honeycomb has 45 relations, while 8-orthoplex has 43. As they have in common 19, the Jaccard index is 21.59% = 19 / (45 + 43).

References

This article shows the relationship between 5 21 honeycomb and 8-orthoplex. To access each article from which the information was extracted, please visit:

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