Tesseractic honeycomb honeycomb explained

bgcolor=#e7dcc3 colspan=2Tesseractic honeycomb honeycomb
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TypeHyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram

5-faces
4-faces
Cells
Faces
Cell figure
Face figure
Edge figure
Vertex figure
DualOrder-4 24-cell honeycomb honeycomb
Coxeter group5, [3,4,3,3,4]
PropertiesRegular
In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb.

Related honeycombs

It is related to the regular Euclidean 4-space tesseractic honeycomb, .

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

See also

References