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Runcicantellated 24-cell honeycomb

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Shape in Euclidean geometry
Runcicantellated 24-cell honeycomb
(No image)
Type Uniform 4-honeycomb
Schläfli symbols t0,2,3{3,4,3,3}
s2,3{3,4,3,3}
Coxeter diagrams
4-face type t0,1,3{3,3,4}

2t{3,3,4}
{3}x{3}
t{3,3}x{}

Cell type
Face type
Vertex figure
Coxeter groups F ~ 4 {\displaystyle {\tilde {F}}_{4}} ,
Properties Vertex transitive

In four-dimensional Euclidean geometry, the runcicantellated 24-cell honeycomb is a uniform space-filling honeycomb.

Alternate names

  • Runcicantellated icositetrachoric tetracomb/honeycomb
  • Prismatorhombated icositetrachoric tetracomb (pricot)
  • Great diprismatodisicositetrachoric 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 118
  • Klitzing, Richard. "4D Euclidean tesselations". o3x3x4o3x - apricot - O118
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 3 3 Hexagonal
E Uniform convex honeycomb 0 δ4 4 4
E Uniform 4-honeycomb 0 δ5 5 5 24-cell honeycomb
E Uniform 5-honeycomb 0 δ6 6 6
E Uniform 6-honeycomb 0 δ7 7 7 222
E Uniform 7-honeycomb 0 δ8 8 8 133331
E Uniform 8-honeycomb 0 δ9 9 9 152251521
E Uniform 9-honeycomb 0 δ10 10 10
E Uniform 10-honeycomb 0 δ11 11 11
E Uniform (n-1)-honeycomb 0 δn n n 1k22k1k21
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