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33 relations: Alternated hypercubic honeycomb, Apeirogon, Complex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Crystallographic restriction theorem, Cubic honeycomb, Cubic honeycomb honeycomb, Cyclotruncated simplectic honeycomb, Demihypercube, Dual polyhedron, F4 (mathematics), Honeycomb (geometry), Hypercube, List of mathematical shapes, List of polygons, polyhedra and polytopes, List of regular polytopes and compounds, Omnitruncated simplectic honeycomb, OpenSimplex noise, Polytope compound, Quarter hypercubic honeycomb, Simplectic honeycomb, Simplex, Simplex noise, Tesseractic honeycomb, Tesseractic honeycomb honeycomb, Uniform 10-polytope, Uniform 6-polytope, 5-cubic honeycomb, 6-cubic honeycomb, 7-cubic honeycomb, 8-cubic honeycomb.
Alternated hypercubic honeycomb
In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation.
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Apeirogon
In geometry, an apeirogon (from the Greek word ἄπειρος apeiros, "infinite, boundless" and γωνία gonia, "angle") is a generalized polygon with a countably infinite number of sides.
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Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.
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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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Cross-polytope
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
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Crystallographic restriction theorem
The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold.
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Cubic honeycomb
The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells.
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Cubic honeycomb honeycomb
In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs).
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Cyclotruncated simplectic honeycomb
In geometry, the cyclotruncated simplectic honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the _n affine Coxeter group.
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Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.
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Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, 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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F4 (mathematics)
In mathematics, F4 is the name of a Lie group and also its Lie algebra f4.
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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.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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List of mathematical shapes
Following is a list of some mathematically well-defined shapes.
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List of polygons, polyhedra and polytopes
A polytope is a geometric object with flat sides, which exists in any general number of dimensions.
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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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Omnitruncated simplectic honeycomb
In geometry an omnitruncated simplectic honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry of the _n affine Coxeter group.
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OpenSimplex noise
OpenSimplex noise is an n-dimensional gradient noise function that was developed in order to overcome the patent-related issues surrounding Simplex noise, while continuing to also avoid the visually-significant directional artifacts characteristic of Perlin noise.
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Polytope compound
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
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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.
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Simplectic honeycomb
In geometry, the simplectic honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the _n affine Coxeter group symmetry.
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Simplex noise
Simplex noise is a method for constructing an n-dimensional noise function comparable to Perlin noise ("classic" noise) but with fewer directional artifacts and, in higher dimensions, a lower computational overhead.
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Tesseractic honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol, and constructed by a 4-dimensional packing of tesseract facets.
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Tesseractic honeycomb honeycomb
In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs).
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Uniform 10-polytope
In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.
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Uniform 6-polytope
In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.
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5-cubic honeycomb
The 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space.
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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.
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7-cubic honeycomb
The 7-cubic honeycomb or hepteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 7-space.
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8-cubic honeycomb
The 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space.
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Redirects here:
Dekeractic honeycomb, Enneractic honeycomb, Hypercube honeycomb, Hypercubic lattice.
References
[1] https://en.wikipedia.org/wiki/Hypercubic_honeycomb
