Small stellated 120-cell honeycomb

In the geometry of hyperbolic 4-space, the small stellated 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5/2,5,3,3}, it has three small stellated 120-cells around each face. It is dual to the pentagrammic-order 600-cell honeycomb.

Small stellated 120-cell honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol	{5/2,5,3,3}
Coxeter diagram
4-faces	{5/2,5,3}
Cells	{5/2,5}
Faces	{5/2}
Face figure	{3}
Edge figure	{3,3}
Vertex figure	{5,3,3}
Dual	Pentagrammic-order 600-cell honeycomb
Coxeter group	H4, [5,3,3,3]
Properties	Regular

It can be seen as a stellation of the 120-cell honeycomb, and is thus analogous to the three-dimensional small stellated dodecahedron {5/2,5} and four-dimensional small stellated 120-cell {5/2,5,3}. It has density 5.

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)