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Stericated 24-cell honeycomb

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Stericated 24-cell honeycomb
Stericated 16-cell honeycomb
(No image)
Type Uniform 4-honeycomb
Schläfli symbol t04{3,4,3,3}
Coxeter-Dynkin diagrams
4-face type {3,4,3}
{3,3,4}
{3,4}x{}
{3,3}x{}
{3}x{3}
Cell type {3,4}
{3,3}
{3}x{}
Face type {3}, {4}
Vertex figure
Coxeter groups F ~ 4 {\displaystyle {\tilde {F}}_{4}} ,
Properties Vertex transitive

In four-dimensional Euclidean geometry, the stericated 24-cell honeycomb (or stericated 16-cell honeycomb) is a uniform space-filling honeycomb. It can be seen as a sterication of the regular 24-cell honeycomb, containing 24-cell, 16-cell, octahedral prism, tetrahedral prism, and 3-3 duoprism cells.

Alternate names

  • Stericated icositetrachoric/hexadecaachoric tetracomb/honeycomb
  • Small cellated demitesseractic tetracomb (scicot)

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 121 (Wrongly named runcinated icositetrachoric honeycomb)
  • Klitzing, Richard. "4D Euclidean tesselations". x3o3o4o3x - scicot - O121
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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