Great 120-cell honeycomb

In the geometry of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face. It is dual to the order-5 icosahedral 120-cell honeycomb.

Great 120-cell honeycomb
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TypeHyperbolic regular honeycomb
Schläfli symbol{5,5/2,5,3}
Coxeter diagram
4-faces {5,5/2,5}
Cells {5,5/2}
Faces {5}
Face figure {3}
Edge figure {5,3}
Vertex figure {5/2,5,3}
DualOrder-5 icosahedral 120-cell honeycomb
Coxeter groupH4, [5,3,3,3]
PropertiesRegular

It can be seen as a greatening of the 120-cell honeycomb, and is thus analogous to the three-dimensional great dodecahedron {5,5/2} and four-dimensional great 120-cell {5,5/2,5}. It has density 10.

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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