Small stellated 120-cell honeycomb: Difference between revisions

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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

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.

It can be seen as a stellation of the 120-cell honeycomb, and is such 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.

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 '''small stellated 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5/2,5,3,3}, it has three [[small stellated 120-cell]]s around each edge. It is [[dual polytope|dual]] to the [[pentagrammic-order 600-cell honeycomb]].
+In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''small stellated 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5/2,5,3,3}, it has three [[small stellated 120-cell]]s around each face. It is [[dual polytope|dual]] to the [[pentagrammic-order 600-cell honeycomb]].
 It can be seen as a [[stellation]] of the [[120-cell honeycomb]], and is such 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 (polytope)|density]] 5.