Order-5 icosahedral 120-cell honeycomb

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

Order-5 icosahedral 120-cell honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol	{3,5,5/2,5}
Coxeter diagram
4-faces	{3,5,5/2}
Cells	{3,5}
Faces	{3}
Face figure	{5}
Edge figure	{5/2,5}
Vertex figure	{5,5/2,5}
Dual	Great 120-cell honeycomb
Coxeter group	H4, [5,3,3,3]
Properties	Regular

It can be constructed by replacing the great dodecahedral cells of the great 120-cell honeycomb with their icosahedral convex hulls, thus replacing the great 120-cells with icosahedral 120-cells. It is thus analogous to the four-dimensional icosahedral 120-cell. It has density 10.

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)