Order-4 120-cell honeycomb

In the geometry of hyperbolic 4-space, the order-4 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,4}, it has four 120-cells around each face. Its dual is the order-5 tesseractic honeycomb, {4,3,3,5}.

Order-4 120-cell honeycomb
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TypeHyperbolic regular honeycomb
Schläfli symbol{5,3,3,4}
{5,3,31,1}
Coxeter diagram
=
4-faces {5,3,3}
Cells {5,3}
Faces {5}
Face figure {4}
Edge figure {3,4}
Vertex figure {3,3,4}
DualOrder-5 tesseractic honeycomb
Coxeter groupBH4, [5,3,3,4]
PropertiesRegular

It is related to the (order-3) 120-cell honeycomb, and order-5 120-cell honeycomb.

It is analogous to the order-4 dodecahedral honeycomb and order-4 pentagonal tiling.

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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