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Gosset–Elte figures and Rectified 5-simplexes

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

Difference between Gosset–Elte figures and Rectified 5-simplexes

Gosset–Elte figures vs. Rectified 5-simplexes

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. In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.

Similarities between Gosset–Elte figures and Rectified 5-simplexes

Gosset–Elte figures and Rectified 5-simplexes have 21 things in common (in Unionpedia): Coxeter group, Emanuel Lodewijk Elte, Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Octahedron, Projection (linear algebra), Rectification (geometry), Rectified 5-cell, Rectified 6-cubes, Tetrahedron, Uniform polytope, Vertex figure, Wythoff construction, 1 22 polytope, 2 22 honeycomb, 2 31 polytope, 3 31 honeycomb, 5-cell, 5-simplex, 6-demicube.

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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Emanuel Lodewijk Elte

Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.

Emanuel Lodewijk Elte and Gosset–Elte figures · Emanuel Lodewijk Elte and Rectified 5-simplexes · See more »

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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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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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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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.

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Rectified 5-cell

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

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Rectified 6-cubes

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.

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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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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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1 22 polytope

In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.

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2 22 honeycomb

In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.

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2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

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3 31 honeycomb

In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.

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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-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

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The list above answers the following questions

Gosset–Elte figures and Rectified 5-simplexes Comparison

Gosset–Elte figures has 77 relations, while Rectified 5-simplexes has 44. As they have in common 21, the Jaccard index is 17.36% = 21 / (77 + 44).

References

This article shows the relationship between Gosset–Elte figures and Rectified 5-simplexes. To access each article from which the information was extracted, please visit:

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