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...

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...

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

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

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

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

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...

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

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...

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

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

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

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

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...

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...

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

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...

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...

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

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

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

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...

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...

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...

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...

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

are 9 uniform honeycombs that include triangular prism cells: Gyroelongated alternated cubic honeycomb, elongated alternated cubic honeycomb, gyrated triangular...

3-space honeycomb or 4-polytope = 0 {\displaystyle =0}  : Euclidean 3-space honeycomb < 0 {\displaystyle <0}  : Hyperbolic 3-space honeycomb These constraints...