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Uniform 7-polytope and Uniform 8-polytope

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

Difference between Uniform 7-polytope and Uniform 8-polytope

Uniform 7-polytope vs. Uniform 8-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.

Similarities between Uniform 7-polytope and Uniform 8-polytope

Uniform 7-polytope and Uniform 8-polytope have 22 things in common (in Unionpedia): Alicia Boole Stott, Betti number, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, E7 (mathematics), Euler characteristic, Face (geometry), Facet (geometry), Factorial, Geometry, Harold Scott MacDonald Coxeter, Homology (mathematics), Isogonal figure, Messenger of Mathematics, Norman Johnson (mathematician), Polytope, Schläfli symbol, Thorold Gosset, Uniform polytope, Vertex figure, 6-polytope.

Alicia Boole Stott

Alicia Boole Stott (8 June 1860 – 17 December 1940) was an Irish-English mathematician.

Alicia Boole Stott and Uniform 7-polytope · Alicia Boole Stott and Uniform 8-polytope · See more »

Betti number

In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.

Betti number and Uniform 7-polytope · Betti number and Uniform 8-polytope · See more »

Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

Coxeter element and Uniform 7-polytope · Coxeter element and Uniform 8-polytope · See more »

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).

Coxeter group and Uniform 7-polytope · Coxeter group and Uniform 8-polytope · See more »

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).

Coxeter–Dynkin diagram and Uniform 7-polytope · Coxeter–Dynkin diagram and Uniform 8-polytope · See more »

E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.

E7 (mathematics) and Uniform 7-polytope · E7 (mathematics) and Uniform 8-polytope · See more »

Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

Euler characteristic and Uniform 7-polytope · Euler characteristic and Uniform 8-polytope · See more »

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.

Face (geometry) and Uniform 7-polytope · Face (geometry) and Uniform 8-polytope · See more »

Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

Facet (geometry) and Uniform 7-polytope · Facet (geometry) and Uniform 8-polytope · See more »

Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

Factorial and Uniform 7-polytope · Factorial and Uniform 8-polytope · 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.

Geometry and Uniform 7-polytope · Geometry and Uniform 8-polytope · See more »

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

Harold Scott MacDonald Coxeter and Uniform 7-polytope · Harold Scott MacDonald Coxeter and Uniform 8-polytope · See more »

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

Homology (mathematics) and Uniform 7-polytope · Homology (mathematics) and Uniform 8-polytope · See more »

Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

Isogonal figure and Uniform 7-polytope · Isogonal figure and Uniform 8-polytope · See more »

Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

Messenger of Mathematics and Uniform 7-polytope · Messenger of Mathematics and Uniform 8-polytope · See more »

Norman Johnson (mathematician)

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

Norman Johnson (mathematician) and Uniform 7-polytope · Norman Johnson (mathematician) and Uniform 8-polytope · See more »

Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

Polytope and Uniform 7-polytope · Polytope and Uniform 8-polytope · See more »

Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

Schläfli symbol and Uniform 7-polytope · Schläfli symbol and Uniform 8-polytope · See more »

Thorold Gosset

John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.

Thorold Gosset and Uniform 7-polytope · Thorold Gosset and Uniform 8-polytope · See more »

Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

Uniform 7-polytope and Uniform polytope · Uniform 8-polytope and Uniform 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.

Uniform 7-polytope and Vertex figure · Uniform 8-polytope and Vertex figure · See more »

6-polytope

In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets.

6-polytope and Uniform 7-polytope · 6-polytope and Uniform 8-polytope · See more »

The list above answers the following questions

Uniform 7-polytope and Uniform 8-polytope Comparison

Uniform 7-polytope has 79 relations, while Uniform 8-polytope has 61. As they have in common 22, the Jaccard index is 15.71% = 22 / (79 + 61).

References

This article shows the relationship between Uniform 7-polytope and Uniform 8-polytope. To access each article from which the information was extracted, please visit:

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