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词条 Order-5 120-cell honeycomb
释义

  1. Related honeycombs

  2. Birectified order-5 120-cell honeycomb

  3. See also

  4. References

Order-5 120-cell honeycomb
(No image)
TypeHyperbolic regular honeycomb
Schläfli symbol{5,3,3,5}
Coxeter diagramnode_1|5|node|3|node|3|node|5|node}}
4-faces {5,3,3}
Cells {5,3}
Faces {5}
Face figure {5}
Edge figure {3,5}
Vertex figure {3,3,5}
DualSelf-dual
Coxeter groupK}}4, [5,3,3,5]
PropertiesRegular

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

Related honeycombs

It is related to the (order-3) 120-cell honeycomb, and order-4 120-cell honeycomb. It is analogous to the order-5 dodecahedral honeycomb and order-5 pentagonal tiling.

Birectified order-5 120-cell honeycomb

The birectified order-5 120-cell honeycomb {{CDD|node|5|node|3|node_1|3|node|5|node}} constructed by all rectified 600-cells, with octahedron and icosahedron cells, and triangle faces with a 5-5 duoprism vertex figure and has extended symmetry [[5,3,3,5]].

See also

  • List of regular polytopes

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)

2 : Honeycombs (geometry)|Self-dual tilings

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