Order-5 5-cell honeycomb: Difference between revisions

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Order-5 5-cell honeycomb
(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol	{3,3,3,5}
Coxeter diagram
4-faces	{3,3,3}
Cells	{3,3}
Faces	{3}
Face figure	{5}
Edge figure	{3,5}
Vertex figure	{3,3,5}
Dual	120-cell honeycomb
Coxeter group	H₄, [5,3,3,3]
Properties	Regular

In the geometry of hyperbolic 4-space, the order-5 5-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {3,3,3,5}, it has five 5-cells around each face. Its dual is the 120-cell honeycomb, {5,3,3,3}.

Related honeycombs

It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3,5}.

It is topologically similar to the finite 5-orthoplex, {3,3,3,4}, and 5-simplex, {3,3,3,3}.

It is analogous to the 600-cell, {3,3,5}, and icosahedron, {3,5}.

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)

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 |bgcolor=#ffffff align=center colspan=2|(No image)
 |-
-|bgcolor=#e7dcc3|Type||[[List_of_regular_polytopes#Tessellations_of_hyperbolic_3-space|Hyperbolic regular honeycomb]]
+|bgcolor=#e7dcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]
 |-
 |bgcolor=#e7dcc3|[[Schläfli symbol]]||{3,3,3,5}
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 |bgcolor=#e7dcc3|Edge figure||[[File:Icosahedron.svg|30px]] [[Icosahedron|{3,5}]]
 |-
-|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Schlegel_wireframe_600-cell.png|50px]] [[600-cell|{3,3,5}]]
+|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Schlegel_wireframe_600-cell_vertex-centered.png|50px]] [[600-cell|{3,3,5}]]
 |-
 |bgcolor=#e7dcc3|Dual||[[120-cell honeycomb]]
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 |bgcolor=#e7dcc3|Properties||Regular
 |}
-In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 5-cell honeycomb''' is one of five compact [[regular polytope|regular]] space-filling [[tessellation]]s (or [[honeycomb (geometry)|honeycombs]]). With [[Schläfli symbol]] {3,3,3,5}, it has five [[5-cell]]s around each edge. Its [[dual polytope|dual]] is the [[120-cell honeycomb]], {5,3,3,3}.
+In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 5-cell honeycomb''' is one of five compact [[regular polytope|regular]] space-filling [[tessellation]]s (or [[honeycomb (geometry)|honeycombs]]). With [[Schläfli symbol]] {3,3,3,5}, it has five [[5-cell]]s around each face. Its [[dual polytope|dual]] is the [[120-cell honeycomb]], {5,3,3,3}.
 == Related honeycombs==
+It is related to the [[order-5 tesseractic honeycomb]], {4,3,3,5}, and [[order-5 120-cell honeycomb]], {5,3,3,5}.
 It is topologically similar to the finite [[5-orthoplex]], {3,3,3,4}, and [[5-simplex]], {3,3,3,3}.
+It is analogous to the [[600-cell]], {3,3,5}, and [[icosahedron]], {3,5}.
 == See also ==
@@ Line 37: / Line 41: @@
 == References ==
-*[[H.S.M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp.&nbsp;294–296)
+*[[H.S.M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. {{isbn|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp.&nbsp;294–296)
-*[[H.S.M. Coxeter|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)
+*[[H.S.M. Coxeter|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)
 [[Category:Honeycombs (geometry)]]