Bitruncated tesseractic honeycomb

Bitruncated tesseractic honeycomb
(No image)
Type	Uniform 4-honeycomb
Schläfli symbol	t1,2{4,3,3,4} or 2t{4,3,3,4} t1,2{4,31,1} or 2t{4,31,1} t2,3{4,31,1} q2{4,3,3,3,4}
Coxeter-Dynkin diagram	=
4-face type	Bitruncated tesseract Truncated 16-cell
Cell type	Octahedron Truncated tetrahedron Truncated octahedron
Face type	{3}, {4}, {6}
Vertex figure	Square-pyramidal pyramid
Coxeter group	${\tilde {C}}_{4}$ = [4,3,3,4] ${\tilde {B}}_{4}$ = [4,31,1] ${\tilde {D}}_{4}$ = [31,1,1,1]
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{4,3,3,4} construction.

Other names

• Bitruncated tesseractic tetracomb (batitit)

Related honeycombs

C4 honeycombs B4 honeycombs D4 honeycombs

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, 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] See p318 [2]
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
• Klitzing, Richard. "4D Euclidean tesselations#4D". x3x3x *b3o *b3o , x3x3x *b3o4o , o3x3o *b3x4o , o4x3x3o4o - batitit - O92
• Conway JH, Sloane NJH (1998). Sphere Packings, Lattices and Groups (3rd ed.). ISBN 0-387-98585-9.

Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space	Family	${\tilde {A}}_{n-1}$	${\tilde {C}}_{n-1}$	${\tilde {B}}_{n-1}$	${\tilde {D}}_{n-1}$	${\tilde {G}}_{2}$ / ${\tilde {F}}_{4}$ / ${\tilde {E}}_{n-1}$
E2	Uniform tiling	0[3]	δ3	hδ3	qδ3	Hexagonal
E3	Uniform convex honeycomb	0[4]	δ4	hδ4	qδ4
E4	Uniform 4-honeycomb	0[5]	δ5	hδ5	qδ5	24-cell honeycomb
E5	Uniform 5-honeycomb	0[6]	δ6	hδ6	qδ6
E6	Uniform 6-honeycomb	0[7]	δ7	hδ7	qδ7	222
E7	Uniform 7-honeycomb	0[8]	δ8	hδ8	qδ8	133 • 331
E8	Uniform 8-honeycomb	0[9]	δ9	hδ9	qδ9	152 • 251 • 521
E9	Uniform 9-honeycomb	0[10]	δ10	hδ10	qδ10
E10	Uniform 10-honeycomb	0[11]	δ11	hδ11	qδ11
En−1	Uniform (n−1)-honeycomb	0[n]	δn	hδn	qδn	1k2 • 2k1 • k21