Great 120-cell honeycomb: Difference between revisions

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

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

It can be seen as a greatening of the 120-cell honeycomb, and is thus analogous to the three-dimensional great dodecahedron {5,5/2} and four-dimensional great 120-cell {5,5/2,5}.

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)

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 In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''great 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5,5/2,5,3}, it has three [[great 120-cell]]s around each edge. It is [[dual polytope|dual]] to the [[order-5 icosahedral 120-cell honeycomb]].
+It can be seen as a [[stellation#Naming stellations|greatening]] of the [[120-cell honeycomb]], and is thus analogous to the three-dimensional [[great dodecahedron]] {5,5/2} and four-dimensional [[great 120-cell]] {5,5/2,5}.
 == See also ==