24-cell honeycomb honeycomb

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24-cell honeycomb honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {3,4,3,3,3}
Coxeter diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel branch3.pngCDel splitsplit2.pngCDel node.pngCDel split1.pngCDel nodes.png = CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node g.pngCDel 3g.pngCDel node g.pngCDel 3sg.pngCDel node g.pngCDel 3g.pngCDel node g.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel splitsplit1.pngCDel branch3.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.pngCDel 4a4b.pngCDel nodes.png
5-faces Icositetrachoronic tetracomb.png {3,4,3,3}
4-faces Schlegel wireframe 24-cell.png {3,4,3}
Cells Octahedron.png {3,4}
Faces Regular polygon 3 annotated.svg {3}
Cell figure Regular polygon 3 annotated.svg {3}
Face figure Tetrahedron.png {3,3}
Edge figure Schlegel wireframe 5-cell.png {3,3,3}
Vertex figure 5-cube t0.svg {4,3,3,3}
Dual 5-orthoplex honeycomb
Coxeter group U5, [3,3,3,4,3]
Properties Regular

In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 4-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {3,4,3,3,3}, it has three 24-cell honeycombs around each cell. It is dual to the 5-orthoplex honeycomb.

Related honeycombs[]

It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, and the hyperbolic 5-space order-4 24-cell honeycomb honeycomb.

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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