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Order-5 120-cell honeycomb, the Glossary

In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs).^[1]

24 relations: Coxeter group, Coxeter–Dynkin diagram, Dodecahedron, Dual polyhedron, Duoprism, Geometry, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Hyperbolic space, Icosahedron, List of regular polytopes, Octahedron, Order-4 120-cell honeycomb, Order-5 pentagonal tiling, Pentagon, Rectified 600-cell, Regular polytope, Regular Polytopes (book), Schläfli symbol, Tessellation, Vertex figure, 120-cell, 120-cell honeycomb, 600-cell.
Self-dual tilings

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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In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

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Dodecahedron

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces.

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Dual polyhedron

In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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Duoprism

In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

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Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. Order-5 120-cell honeycomb and honeycomb (geometry) are honeycombs (geometry).

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Hyperbolic space

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to −1.

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Icosahedron

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

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List of regular polytopes

This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces.

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Octahedron

In geometry, an octahedron (octahedra or octahedrons) is a polyhedron with eight faces.

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Order-4 120-cell honeycomb

In the geometry of hyperbolic 4-space, the order-4 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). Order-5 120-cell honeycomb and order-4 120-cell honeycomb are honeycombs (geometry).

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Order-5 pentagonal tiling

In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. Order-5 120-cell honeycomb and order-5 pentagonal tiling are Self-dual tilings.

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Pentagon

In geometry, a pentagon is any five-sided polygon or 5-gon.

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Rectified 600-cell

In geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells.

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Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

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Regular Polytopes (book)

Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter.

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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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Tessellation

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.

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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 (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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120-cell honeycomb

In the geometry of hyperbolic 4-space, the 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). Order-5 120-cell honeycomb and 120-cell honeycomb are honeycombs (geometry).

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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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References

[1] https://en.wikipedia.org/wiki/Order-5_120-cell_honeycomb

Also known as Birectified order-5 120-cell.