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Cantitruncated 24-cell honeycomb

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Cantitruncated 24-cell honeycomb
(No image)
Type Uniform 4-honeycomb
Schläfli symbol tr{3,4,3,3}
Coxeter-Dynkin diagrams
4-face type t{4,3,3}
tr{3,4,3}
{3,3}×{}
Cell type
Face type
Vertex figure
Coxeter groups F ~ 4 {\displaystyle {\tilde {F}}_{4}} ,
Properties Vertex transitive

In four-dimensional Euclidean geometry, the cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract, cantitruncated 24-cell, and tetrahedral prism cells.

Alternate names

  • Cantellated icositetrachoric tetracomb/honeycomb
  • Great rhombated icositetrachoric tetracomb (gricot)
  • Great prismatodisicositetrachoric tetracomb

Related honeycombs

The , , Coxeter group generates 31 permutations of uniform tessellations, 28 are unique in this family and ten are shared in the and families. The alternation (13) is also repeated in other families.

F4 honeycombs
Extended
symmetry		 Extended
diagram		 Order Honeycombs
×1

1, 3, 5, 6, 8,
9, 10, 11, 12

×1

2, 4, 7, 13,
14, 15, 16, 17,
18, 19, 20, 21,
22 23, 24, 25,
26, 27, 28, 29

]
=]
=
=
= 		×4

(2), (4), (7), (13)

See also

Regular and uniform honeycombs in 4-space:

References

  • Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III,
  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 114
  • Klitzing, Richard. "4D Euclidean tesselations". o3o3x4x3x - gricot - O114
Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space Family A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} G ~ 2 {\displaystyle {\tilde {G}}_{2}} / F ~ 4 {\displaystyle {\tilde {F}}_{4}} / E ~ n − 1 {\displaystyle {\tilde {E}}_{n-1}}
E Uniform tiling 0 δ3 hδ3 qδ3 Hexagonal
E Uniform convex honeycomb 0 δ4 hδ4 qδ4
E Uniform 4-honeycomb 0 δ5 hδ5 qδ5 24-cell honeycomb
E Uniform 5-honeycomb 0 δ6 hδ6 qδ6
E Uniform 6-honeycomb 0 δ7 hδ7 qδ7 222
E Uniform 7-honeycomb 0 δ8 hδ8 qδ8 133 • 331
E Uniform 8-honeycomb 0 δ9 hδ9 qδ9 152 • 251 • 521
E Uniform 9-honeycomb 0 δ10 hδ10 qδ10
E Uniform 10-honeycomb 0 δ11 hδ11 qδ11
E Uniform (n-1)-honeycomb 0 δn hδn qδn 1k2 • 2k1 • k21
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