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...

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

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

The order-6 cubic honeycomb is a paracompact regular space-filling tessellation (or honeycomb) in hyperbolic 3-space. It is paracompact because it has...

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

honeycomb Order-4 dodecahedral honeycomb Order-5 dodecahedral honeycomb Order-5 cubic honeycomb Icosahedral honeycomb Order-3 icosahedral honeycomb Order-4...

belong to 4 cells. The tetrahedral disphenoid honeycomb is the dual of the uniform bitruncated cubic honeycomb. Its vertices form the A* 3 / D* 3 lattice...

constructed from 3 orthogonal axes. Its dual is the order-5 cubic honeycomb. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells...

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

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

form, and its dual, the order-6 cubic honeycomb. The order-4 hexagonal tiling honeycomb has a related alternated honeycomb, ↔ , with triangular tiling and...

In geometry, the 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four 5-cubes...

uniform honeycomb Cubic honeycomb Truncated cubic honeycomb Bitruncated cubic honeycomb Cantellated cubic honeycomb Cantitruncated cubic honeycomb Rectified...

hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact...

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

In geometry, the 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space. It is analogous...

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

The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-space. It is analogous to the...

The 7-cubic honeycomb or hepteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 7-space. It is analogous to...

dodecahedral honeycomb, with the rhombic dodecahedra dissected with its center into 12 rhombic pyramids. It is dual to the cantic cubic honeycomb: Architectonic...

constructed from 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...

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...

Gyrated alternated cubic honeycomb (Complex tetroctahedric check), Semiregular E-honeycomb: 521 honeycomb (9-ic check) (8D Euclidean honeycomb), Gosset (1900)...

The triakis truncated tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triakis truncated tetrahedra...

tiling, {4,4}, of the plane and the cubic honeycomb, {4,3,4}, of 3-space. These are all part of the hypercubic honeycomb family of tessellations of the form...

A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate...

cell, and examples of a honeycomb are cubic honeycomb, order-5 cubic honeycomb, order-6 cubic honeycomb, and order-7 cubic honeycomb. The cube can be constructed...

figure is a regular tetrahedron {3,3}. Also the vertex figure for a cubic honeycomb {4,3,4}, the vertex figure is a regular octahedron {3,4}. Since the...

geometry of hyperbolic 3-space, the order-7 cubic honeycomb is a regular space-filling tessellation (or honeycomb). With Schläfli symbol {4,3,7}, it has seven...

place of all lower-dimensional elements. For example, an expanded cubic honeycomb has cubic cells centered on the original cubes, on the original faces, on...