The order-6 dodecahedral honeycomb is one of 11 paracompact regular honeycombs in hyperbolic 3-space. It is paracompact because it has vertex figures composed...

hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) of hyperbolic 3-space...

20 cubes around each vertex. It is dual with the order-4 dodecahedral honeycomb. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional...

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

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

its regular dual, the order-6 dodecahedral honeycomb. The order-5 hexagonal tiling honeycomb has a related alternation honeycomb, represented by ↔ , with...

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

of hyperbolic 3-space, the order-6-4 square honeycomb (or 4,6,4 honeycomb) a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,6...

honeycombs with {p,6,3} Schläfli symbol, and dodecahedral vertex figures: In the geometry of hyperbolic 3-space, the order-6-3 pentagonal honeycomb or...

constructionally related to prismatic uniform honeycombs by truncation operations. They are higher-dimensional analogues of the order-2 apeirogonal tiling and apeirogonal...

honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973...

hexagonal tiling cells: This honeycomb is also related to the 16-cell, cubic honeycomb and order-4 dodecahedral honeycomb, all of which have octahedral...

each vertex, in a regular dodecahedral vertex figure. It is analogous to the 24-cell and the 5-cell. A geometric honeycomb is a space-filling of polyhedral...

120 with a dodecahedral fundamental domain. There are also 23 paracompact Coxeter groups of rank 4 that produce paracompact uniform honeycombs with infinite...

colors of cells. Convex uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes,...

can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb. There are some variations of the rhombic dodecahedron, one of which...

parallelohedra: Cubic honeycomb (or variations: cuboid, rhombic hexahedron or parallelepiped) Hexagonal prismatic honeycomb Rhombic dodecahedral honeycomb Elongated...

honeycombs with {p,5,3} Schläfli symbol, and dodecahedral vertex figures: In the geometry of hyperbolic 3-space, the order-5-3 pentagonal honeycomb or...

related to the rhombic dodecahedral honeycomb with an elongation of zero. Projected normal to the elongation direction, the honeycomb looks like a square...

projection of the tesseract into three-dimensional space has a rhombic dodecahedral envelope. Two vertices of the tesseract are projected to the origin....

tiling cells. Convex uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes,...

Truncated 5-simplex honeycomb Omnitruncated 5-simplex honeycomb C ~ 5 {\displaystyle {\tilde {C}}_{5}} There are 35 uniform honeycombs, including: Regular...

dodecahedral honeycomb Weaire–Phelan structure Convex uniform honeycombs in hyperbolic space Order-4 dodecahedral honeycomb Order-5 cubic honeycomb Order-5...

(120 dodecahedral cells) Order-3 120-cell honeycomb, {5, 3, 3, 3} (tessellates hyperbolic 4-space (∞ 120-cell facets) The facets of each dodecahedral pentagonal...

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

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

respectively the order-6 tetrahedral honeycomb, order-6 cubic honeycomb, order-4 octahedral honeycomb, and order-6 dodecahedral honeycomb; here the order refers...

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

cases include the Euclidean cubic honeycomb {4,3,4} with cubic cells, and compact hyperbolic {5,3,4} with dodecahedral cells, and paracompact {6,3,4} with...

cross-section through xi = n is a rhombic dodecahedral honeycomb, and the cross-section through xi = n + ⁠1/2⁠ is a cubic honeycomb. As the hyperplane moves through...