5-orthoplex and Coxeter notation

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

Difference between 5-orthoplex and Coxeter notation

5-orthoplex vs. Coxeter notation

In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces. In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

Similarities between 5-orthoplex and Coxeter notation

5-orthoplex and Coxeter notation have 9 things in common (in Unionpedia): Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Schläfli symbol, Tetrahedron, 5-cell.

Coxeter element

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

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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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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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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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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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The list above answers the following questions

What 5-orthoplex and Coxeter notation have in common
What are the similarities between 5-orthoplex and Coxeter notation

5-orthoplex and Coxeter notation Comparison

5-orthoplex has 39 relations, while Coxeter notation has 82. As they have in common 9, the Jaccard index is 7.44% = 9 / (39 + 82).

References

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

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