Tesseractic honeycomb honeycomb

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Tesseractic honeycomb honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {4,3,3,4,3}
{4,3,31,1,1}
Coxeter diagram CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel splitsplit1.pngCDel branch3.pngCDel node.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node g.pngCDel 3sg.pngCDel node g.png
CDel nodes 10r.pngCDel 4a4b.pngCDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.png
5-faces Tesseractic tetracomb.png {4,3,3,4}
4-faces Schlegel wireframe 8-cell.png {4,3,3}
Cells Hexahedron.png {4,3}
Faces Regular polygon 4 annotated.svg {4}
Cell figure Regular polygon 3 annotated.svg {3}
Face figure Hexahedron.png {4,3}
Edge figure Schlegel wireframe 24-cell.png {3,4,3}
Vertex figure Demitesseractic tetra hc.png {3,3,4,3}
Dual Order-4 24-cell honeycomb honeycomb
Coxeter group R5, [3,4,3,3,4]
Properties Regular

In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {4,3,3,4,3}, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb.

Related honeycombs[]

It is related to the regular Euclidean 4-space tesseractic honeycomb, {4,3,3,4}.

It is analogous to the paracompact cubic honeycomb honeycomb, {4,3,4,3}, in 4-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.

See also[]

  • List of regular polytopes

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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