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.pngCDel 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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