Cubic honeycomb honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol	{4,3,4,3} {4,31,1,1}
Coxeter diagram	↔ ↔
4-faces	{4,3,4}
Cells	{4,3}
Faces	{4}
Face figure	{3}
Edge figure	{4,3}
Vertex figure	{3,4,3}
Dual	Order-4 24-cell honeycomb
Coxeter group	R4, [4,3,4,3]
Properties	Regular

In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 3-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {4,3,4,3}, it has three cubic honeycombs around each face, and with a {3,4,3} vertex figure. It is dual to the order-4 24-cell honeycomb.

Related honeycombs

It is related to the Euclidean 4-space 16-cell honeycomb, {3,3,4,3}, which also has a 24-cell vertex figure.

It is analogous to the paracompact tesseractic honeycomb honeycomb, {4,3,3,4,3}, in 5-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.