Bitruncated 16-cell honeycomb

Bitruncated 16-cell honeycomb
(No image)
Type	Uniform honeycomb
Schläfli symbol	t1,2{3,3,4,3} h2,3{4,3,3,4} 2t{3,3^1,1,1}
Coxeter-Dynkin diagram	= =
4-face type	Truncated 24-cell Bitruncated tesseract
Cell type	Cube Truncated octahedron Truncated tetrahedron
Face type	{3}, {4}, {6}
Vertex figure	triangular duopyramid
Coxeter group	${\tilde{F}}_4$ = [3,3,4,3] ${\tilde{B}}_4$ = [4,3,3^1,1] ${\tilde{D}}_4$ = [3^1,1,1,1]
Dual	?
Properties	vertex-transitive

In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.

Symmetry constructions

There are 3 different symmetry constructions, all with 3-3 duopyramid vertex figures. The ${\tilde{B}}_4$ symmetry doubles on ${\tilde{D}}_4$ in three possible ways, while ${\tilde{F}}_4$ contains the highest symmetry.

Affine Coxeter group	${\tilde{F}}_4$ [3,3,4,3]	${\tilde{B}}_4$ [4,3,3^1,1]	${\tilde{D}}_4$ [3^1,1,1,1]
Coxeter diagram
4-faces

See also

Regular and uniform honeycombs in 4-space:

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

Notes

References

• 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, [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)
• Richard Klitzing, 4D, Euclidean tesselations x3x3x *b3x *b3o, x3x3o *b3x4o, o3x3x4o3o - bithit - O107