Bitruncated tesseractic honeycomb explained

bgcolor=#e7dcc3 colspan=2	Bitruncated tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Uniform 4-honeycomb
Schläfli symbol	t1,2 or 2t t1,2 or 2t t2,3 q2
Coxeter-Dynkin diagram	=
4-face type
Cell type
Face type	,,
Vertex figure	Square-pyramidal pyramid
Coxeter group	{\tilde{C}} _{4} = [4,3,3,4] {\tilde{B}} _{4} = [4,3<sup>1,1</sup>] {\tilde{D}} _{4} = [3<sup>1,1,1,1</sup>]
Dual
Properties	vertex-transitive

In four-dimensional Euclidean geometry, the bitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic honeycomb from its q₂ construction.

Other names

• Bitruncated tesseractic tetracomb (batitit)

See also

Regular and uniform honeycombs in 4-space:

• Tesseractic honeycomb
• Demitesseractic honeycomb
• 24-cell honeycomb
• Truncated 24-cell honeycomb
• Snub 24-cell honeycomb
• 5-cell honeycomb
• Truncated 5-cell honeycomb
• Omnitruncated 5-cell honeycomb

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, 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] See p318 https://books.google.com/books?id=fUm5Mwfx8rAC&dq=%22quarter+cubic+honeycomb%22+q%7B4%2C3%2C4%7D&pg=PA318
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
• x3x3x *b3o *b3o, x3x3x *b3o4o, o3x3o *b3x4o, o4x3x3o4o - batitit - O92
• Book: Conway JH, Sloane NJH . 1998 . Sphere Packings, Lattices and Groups . 3rd . 0-387-98585-9 . registration .