Order-5 120-cell honeycomb explained

bgcolor=#e7dcc3 colspan=2	Order-5 120-cell honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram
4-faces
Cells
Faces
Face figure
Edge figure
Vertex figure
Dual	Self-dual
Coxeter group	4, [5,3,3,5]
Properties	Regular

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, it has five 120-cells around each face. It is self-dual. It also has 600 120-cells around each vertex.

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 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. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
• Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)