Order-4 120-cell honeycomb

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

Order-4 120-cell honeycomb
(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol	{5,3,3,4} {5,3,31,1}
Coxeter diagram	=
4-faces	{5,3,3}
Cells	{5,3}
Faces	{5}
Face figure	{4}
Edge figure	{3,4}
Vertex figure	{3,3,4}
Dual	Order-5 tesseractic honeycomb
Coxeter group	BH4, [5,3,3,4]
Properties	Regular

Related honeycombs

It is related to the (order-3) 120-cell honeycomb, and order-5 120-cell honeycomb.

See also

• List of regular polytopes

References

• 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)