Order-4 24-cell honeycomb

In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two 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 {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.

Order-4 24-cell honeycomb
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TypeHyperbolic regular honeycomb
Schläfli symbol{3,4,3,4}
{3,4,31,1}
Coxeter diagram
4-faces {3,4,3}
Cells {3,4}
Faces {3}
Face figure {4}
Edge figure {3,4}
Vertex figure {4,3,4}
DualCubic honeycomb honeycomb
Coxeter groupR4, [4,3,4,3]
PropertiesRegular

It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell facets.

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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