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Quarter 6-cubic honeycomb

Index Quarter 6-cubic honeycomb

In six-dimensional Euclidean geometry, the quarter 6-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). [1]

Table of Contents

  1. 20 relations: Coxeter group, Coxeter–Dynkin diagram, Cyclotruncated 6-simplex honeycomb, Duoprism, Euclidean geometry, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Isogonal figure, Omnitruncated 6-simplex honeycomb, Pentic 6-cubes, Quarter hypercubic honeycomb, Schläfli symbol, Six-dimensional space, Tessellation, Uniform 7-polytope, Vertex figure, 6-cubic honeycomb, 6-demicube, 6-demicubic honeycomb, 6-simplex honeycomb.

  2. 7-polytopes

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 a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

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Cyclotruncated 6-simplex honeycomb

In six-dimensional Euclidean geometry, the cyclotruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb). Quarter 6-cubic honeycomb and cyclotruncated 6-simplex honeycomb are 7-polytopes and honeycombs (geometry).

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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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Euclidean geometry

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.

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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. Quarter 6-cubic honeycomb and honeycomb (geometry) are honeycombs (geometry).

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Isogonal figure

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

See Quarter 6-cubic honeycomb and Isogonal figure

Omnitruncated 6-simplex honeycomb

In six-dimensional Euclidean geometry, the omnitruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb). Quarter 6-cubic honeycomb and omnitruncated 6-simplex honeycomb are 7-polytopes and honeycombs (geometry).

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Pentic 6-cubes

In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.

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Quarter hypercubic honeycomb

In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. Quarter 6-cubic honeycomb and quarter hypercubic honeycomb are honeycombs (geometry).

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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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Six-dimensional space

Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space.

See Quarter 6-cubic honeycomb and Six-dimensional space

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.

See Quarter 6-cubic honeycomb and Tessellation

Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Quarter 6-cubic honeycomb and Uniform 7-polytope are 7-polytopes.

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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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6-cubic honeycomb

The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-space. Quarter 6-cubic honeycomb and 6-cubic honeycomb are 7-polytopes and honeycombs (geometry).

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6-demicube

In geometry, a 6-demicube or demihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

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6-demicubic honeycomb

The 6-demicubic honeycomb or demihexeractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 6-space. Quarter 6-cubic honeycomb and 6-demicubic honeycomb are 7-polytopes and honeycombs (geometry).

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6-simplex honeycomb

In six-dimensional Euclidean geometry, the 6-simplex honeycomb is a space-filling tessellation (or honeycomb). Quarter 6-cubic honeycomb and 6-simplex honeycomb are 7-polytopes and honeycombs (geometry).

See Quarter 6-cubic honeycomb and 6-simplex honeycomb

See also

7-polytopes

References

[1] https://en.wikipedia.org/wiki/Quarter_6-cubic_honeycomb