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Icosahedral 120-cell

Index Icosahedral 120-cell

In geometry, the icosahedral 120-cell, polyicosahedron, faceted 600-cell or icosaplex is a regular star 4-polytope with Schläfli symbol. [1]

31 relations: Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Edmund Hess, Faceting, Geometry, Grand 120-cell, Great 120-cell, Great dodecahedron, Great grand stellated 120-cell, Harold Scott MacDonald Coxeter, Icosahedron, John Horton Conway, Kepler–Poinsot polyhedron, List of regular polytopes and compounds, Orthographic projection, Pentagonal polytope, Pentagram, Projection (linear algebra), Regular 4-polytope, Schläfli symbol, Small stellated 120-cell, Small stellated dodecahedron, Star polygon, Star polyhedron, Tetrahedron, Triangle, Vertex arrangement, Vertex figure, 120-cell, 600-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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Edmund Hess

Edmund Hess (17 February 1843 – 24 December 1903) was a German mathematician who discovered several regular polytopes.

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Faceting

Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.

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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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Grand 120-cell

In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol.

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Great 120-cell

In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol.

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Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

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Great grand stellated 120-cell

In geometry, the great grand stellated 120-cell or great grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol, one of 10 regular Schläfli-Hess 4-polytopes.

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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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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

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List of regular polytopes and compounds

This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Pentagonal polytope

In geometry, a pentagonal polytope is a regular polytope in n dimensions constructed from the H''n'' Coxeter group.

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Pentagram

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

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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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Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

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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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Small stellated 120-cell

In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol.

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Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

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Star polygon

In geometry, a star polygon is a type of non-convex polygon.

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Star polyhedron

In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.

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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 arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

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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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120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

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600-cell

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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Redirects here:

Faceted 600-cell, Faceted hexacosichoron.

References

[1] https://en.wikipedia.org/wiki/Icosahedral_120-cell

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