120-cell honeycomb

120-cell honeycomb
(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol	{5,3,3,3}
Coxeter diagram
4-faces	{5,3,3}
Cells	{5,3}
Faces	{5}
Face figure	{3}
Edge figure	{3,3}
Vertex figure	{3,3,3}
Dual	Order-5 5-cell honeycomb
Coxeter group	H4, [5,3,3,3]
Properties	Regular

In the geometry of hyperbolic 4-space, the 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,3}, it has three 120-cells around each face. Acronym: hitte^[1]

Its dual is the order-5 5-cell honeycomb, {3,3,3,5}.

Related honeycombs

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

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

It is analogous to the 120-cell, {5,3,3}, and dodecahedron, {5,3}.

See also

• List of regular polytopes
• Great 120-cell honeycomb

Notes

1. Klitzing, (o3o3o3o5x - hitte).

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, pp. 212–213)
• Klitzing, Richard. "4D Tetracombs". o3o3o3o5x - hitte