5-orthoplex honeycomb

5-orthoplex honeycomb
(No image)
TypeHyperbolic regular honeycomb
Schläfli symbol{3,3,3,4,3}
Coxeter diagram
=
5-faces {3,3,3,4}
4-faces {3,3,3}
Cells {3,3}
Faces {3}
Cell figure {3}
Face figure {4,3}
Edge figure {3,4,3}
Vertex figure {3,3,4,3}
Dual24-cell honeycomb honeycomb
Coxeter groupU5, [3,3,3,4,3]
PropertiesRegular

In the geometry of hyperbolic 5-space, the 5-orthoplex 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 {3,3,3,4,3}, it has three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb.

Related honeycombs

It is related to the regular Euclidean 4-space 16-cell honeycomb, {3,3,4,3}, with 16-cell (4-orthoplex) facets, and the regular 4-polytope 24-cell, {3,4,3} with octahedral (3-orthoplex) cell, and cube {4,3}, with (2-orthoplex) square faces.

See also

References

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