16-cell honeycomb honeycomb

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16-cell honeycomb honeycomb
(No image)
Type Hyperbolic regular honeycomb
Schläfli symbol {3,3,4,3,3}
Coxeter diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-faces Demitesseractic tetra hc.png {3,3,4,3}
4-faces Schlegel wireframe 16-cell.png {3,3,4}
Cells Tetrahedron.png {3,3}
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 8-cell.png {4,3,3}
Vertex figure Icositetrachoronic tetracomb.png {3,4,3,3}
Dual self-dual
Coxeter group X5, [3,3,4,3,3]
Properties Regular

In the geometry of hyperbolic 5-space, the 16-cell 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 {3,3,4,3,3}, it has three 16-cell honeycombs around each cell. It is self-dual.

Related honeycombs[edit]

It is related to the regular Euclidean 4-space 16-cell honeycomb, {3,3,4,3}.

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)