Order-4 24-cell honeycomb

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Order-4 24-cell honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {3,4,3,4}
{3,4,31,1}
Coxeter diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel split1.pngCDel nodes.png ↔ CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node h0.png
4-faces Schlegel wireframe 24-cell.png {3,4,3}
Cells Octahedron.png {3,4}
Faces Regular polygon 3 annotated.svg {3}
Face figure Regular polygon 4 annotated.svg {4}
Edge figure Octahedron.png {3,4}
Vertex figure Cubic honeycomb.png {4,3,4}
Dual Cubic honeycomb honeycomb
Coxeter group R4, [4,3,4,3]
Properties Regular

In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two 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 {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.

Related honeycombs[]

It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell 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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