Order-5 5-cell honeycomb

Order-5 5-cell honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {3,3,3,5}
Coxeter diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png
4-faces Schlegel wireframe 5-cell.png {3,3,3}
Cells Tetrahedron.png {3,3}
Faces Regular polygon 3 annotated.svg {3}
Face figure Regular polygon 5 annotated.svg {5}
Edge figure Icosahedron.svg {3,5}
Vertex figure Schlegel wireframe 600-cell vertex-centered.png {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 honeycombsEdit

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 alsoEdit


  • 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)