Order-5 icosahedral 120-cell honeycomb explained

bgcolor=#e7dcc3 colspan=2	Order-5 icosahedral 120-cell honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram
4-faces
Cells
Faces
Face figure
Edge figure
Vertex figure
Dual	Great 120-cell honeycomb
Coxeter group	4, [5,3,3,3]
Properties	Regular

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

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. . (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)