Order-5 tesseractic honeycomb

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Order-5 tesseractic honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {4,3,3,5}
Coxeter diagram CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png
4-faces Schlegel wireframe 8-cell.png {4,3,3}
Cells Hexahedron.png {4,3}
Faces Regular polygon 4 annotated.svg {4}
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 Order-4 120-cell honeycomb
Coxeter group BH4, [5,3,3,4]
Properties Regular

In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.

Related polytopes and honeycombs[edit]

It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.

It is analogous to the order-5 cubic honeycomb {4,3,5} and order-5 square tiling {4,5}.

See also[edit]


  • 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)