Order-5 5-cell honeycomb

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

Order-5 5-cell honeycomb
(No image)
TypeHyperbolic regular honeycomb
Schläfli symbol{3,3,3,5}
Coxeter diagram
4-faces {3,3,3}
Cells {3,3}
Faces {3}
Face figure {5}
Edge figure {3,5}
Vertex figure {3,3,5}
Dual120-cell honeycomb
Coxeter groupH4, [5,3,3,3]
PropertiesRegular

It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3,5}.

It is topologically similar to the finite 5-orthoplex, {3,3,3,4}, and 5-simplex, {3,3,3,3}.

It is analogous to the 600-cell, {3,3,5}, and icosahedron, {3,5}.

gollark: WAR!
gollark: He STOLE TAPE 3?!?!?!?!?!?!?!?!?!?!?!?
gollark: Should we declare war on him?
gollark: Okay, put the computer back under it so it's in the same orientation as before, rightclick it to turn it on, and wait about 10 seconds.
gollark: Is the thing with the hovery clock still above where the computer should go?

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)
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