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1 42 polytope and 8-demicube

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

Difference between 1 42 polytope and 8-demicube

1 42 polytope vs. 8-demicube

In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed.

Similarities between 1 42 polytope and 8-demicube

1 42 polytope and 8-demicube have 21 things in common (in Unionpedia): Convex polytope, Coxeter–Dynkin diagram, Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Petrie polygon, Rectified 7-simplexes, Schläfli symbol, Tetrahedron, Triangle, Uniform 8-polytope, Uniform polytope, Vertex figure, 16-cell, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-demicube.

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–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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Emanuel Lodewijk Elte

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

1 42 polytope and Emanuel Lodewijk Elte · 8-demicube and Emanuel Lodewijk Elte · 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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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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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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Rectified 7-simplexes

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.

1 42 polytope and Rectified 7-simplexes · 8-demicube and Rectified 7-simplexes · 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 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.

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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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16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

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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-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.

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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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6-simplex

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

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7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed.

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The list above answers the following questions

1 42 polytope and 8-demicube Comparison

1 42 polytope has 49 relations, while 8-demicube has 31. As they have in common 21, the Jaccard index is 26.25% = 21 / (49 + 31).

References

This article shows the relationship between 1 42 polytope and 8-demicube. To access each article from which the information was extracted, please visit:

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