Runcinated 24-cell honeycomb explained

bgcolor=#e7dcc3 colspan=2	Runcinated 24-cell honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Uniform 4-honeycomb
Schläfli symbol	t0,3
Coxeter-Dynkin diagrams
4-face type
Cell type	x
Face type	,
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

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, 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, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
  • (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
• o3x3o4o3x - spict - O115