Order-4 24-cell honeycomb honeycomb

In the geometry of hyperbolic 5-space, the order-4 24-cell 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 {3,4,3,3,4}, it has four 24-cell honeycombs around each cell. It is dual to the tesseractic honeycomb honeycomb.

Order-4 24-cell honeycomb honeycomb
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TypeHyperbolic regular honeycomb
Schläfli symbol{3,4,3,3,4}
Coxeter diagram
5-faces {3,4,3,3}
4-faces {3,4,3}
Cells {3,4}
Faces {3}
Cell figure {4}
Face figure {3,4}
Edge figure {3,3,4}
Vertex figure {4,3,3,4}
DualTesseractic honeycomb honeycomb
Coxeter groupR5, [3,4,3,3,4]
PropertiesRegular

It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, as well as the hyperbolic 5-space order-3 24-cell honeycomb honeycomb, {3,4,3,3,3}.

See also

References

  • Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
  • Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
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