The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It...

In the geometry of hyperbolic 3-space, the cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron...

dodecahedral honeycomb which has all 12 faces as rhombi. It is a dual to the vertex-transitive gyrated tetrahedral-octahedral honeycomb. The rhombic pyramidal...

the omnitruncated cubic honeycomb: Architectonic and catoptric tessellation Cubic honeycomb Space frame Tetrahedral-octahedral honeycomb Triakis truncated...

The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells...

In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23...

parallelepiped, copies can fill space, with the cubic honeycomb being special because it is the only regular honeycomb in ordinary (Euclidean) space. Another interesting...

honeycombs are still uniform. There are also other forms based on parallelepiped domains. Two known forms generalise the cubic-octahedral honeycomb,...

cells. Twenty-eight such honeycombs are known: the familiar cubic honeycomb and 7 truncations thereof; the alternated cubic honeycomb and 4 truncations thereof;...

tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular...

in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes. Its dual is the order-5 cubic honeycomb. A geometric honeycomb is a...

The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra (or, equivalently,...

honeycomb (3D) and the 521 honeycomb (8D). Gosset honeycombs: Tetrahedral-octahedral honeycomb or alternated cubic honeycomb (Simple tetroctahedric check)...

Rectified cubic honeycomb Runcitruncated cubic honeycomb Omnitruncated cubic honeycomb Tetrahedral-octahedral honeycomb Truncated alternated cubic honeycomb Cantitruncated...

arrangement produces the tetrahedral-octahedral honeycomb. The HCP arrangement produces the gyrated tetrahedral-octahedral honeycomb. If, instead, every sphere...

The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean...

exactly 16 cubic pyramids. The 24-cell tessellates 4-dimensional space as the 24-cell honeycomb. The dual to the cubic pyramid is an octahedral pyramid,...

hyperbolic geometry, the order-5 cubic honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli...

two regular octahedral pyramids base to base constructs a 16-cell. The 16-cell tessellates 4-dimensional space as the 16-cell honeycomb. Exactly 24 regular...

Rectified cubic honeycomb Runcitruncated cubic honeycomb Omnitruncated cubic honeycomb Tetrahedral-octahedral honeycomb Truncated alternated cubic honeycomb Cantitruncated...

4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken as a unit for...

parallel to the face diagonals of a cube; an example of the honeycomb is the bitruncated cubic honeycomb. More generally, every permutohedron and parallelohedron...

its dual, the order-4 octahedral honeycomb, {3,4,4}. The square tiling honeycomb is part of the order-4 square tiling honeycomb family, as it can be seen...

the vertices lie in parallel realms in which they form alternated cubic honeycombs, the tetrahedra being either tops of the rectified 5-cell or the bases...

demitesseractic honeycomb, h{4,3,3,4}) it is related to the alternated cubic honeycomb. This honeycomb is one of 20 uniform honeycombs constructed by the...

also related to the cubic honeycomb, order-4 dodecahedral honeycomb, and order-4 hexagonal tiling honeycomb which all have octahedral vertex figures. It...

honeycomb and order-4 dodecahedral honeycomb, all of which have octahedral vertex figures. The aforementioned honeycombs are also quasiregular: The rectified...

orthogonal sets of ultra-parallel mirrors in an octahedral fundamental domain: . The order-4 square tiling honeycomb is analogous to the 2D hyperbolic infinite-order...

spherical space. Convex uniform honeycombs in hyperbolic space List of regular polytopes Hyperbolic tetrahedral-octahedral honeycomb Coxeter, Regular Polytopes...

decomposed into square pyramids.) This honeycomb can be considered an elongated version of the tetrahedral-octahedral honeycomb. Critchlow, Keith. Order in Space:...