Runcinated 24-cell honeycomb

Runcinated 24-cell honeycomb
(No image)
Type	Uniform 4-honeycomb
Schläfli symbol	t0,3{3,4,3,3}
Coxeter-Dynkin diagrams
4-face type	t0,3{3,4,3} {3,4,3} {3,4}x{} {3}x{3} 40px
Cell type	{3,4} {3}x{}
Face type	{3}, {4}
Vertex figure
Coxeter groups	${\tilde{F}}_4$, [3,4,3,3]
Properties	Vertex transitive

In four-dimensional Euclidean geometry, the runcinated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 24-cell honeycomb, containing runcinated 24-cell, 24-cell, octahedral prism, and 3-3 duoprism cells.

Alternate names

• Runcinated icositetrachoric tetracomb/honeycomb
• Small prismated icositetrachoric tetracomb (spict)
• Small prismatotetracontaoctachoric tetracomb

Related honeycombs

The [3,4,3,3], , Coxeter group generates 31 permutations of uniform tessellations, 28 are unique in this family and ten are shared in the [4,3,3,4] and [4,3,3^1,1] families. The alternation (13) is also repeated in other families.

F4 honeycombs Extended symmetry Extended diagram Order Honeycombs [3,3,4,3] ×1 1, 3, 5, 6, 8, 9, 10, 11, 12 [3,4,3,3] ×1 2, 4, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 23, 24, 25, 26, 27, 28, 29 [(3,3)[3,3,4,3*]] =[(3,3)[31,1,1,1]] =[3,4,3,3] = = ×4 (2), (4), (7), (13)

See also

Regular and uniform honeycombs in 4-space:

• Tesseractic honeycomb
• 16-cell honeycomb
• 24-cell honeycomb
• Rectified 24-cell honeycomb
• Snub 24-cell honeycomb
• 5-cell honeycomb
• Truncated 5-cell honeycomb
• Omnitruncated 5-cell honeycomb

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 [1]
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 115
• Richard Klitzing, 4D, Euclidean tesselations o3x3o4o3x - spict - O115