bitruncated tesseractic honeycomb

class="wikitable" align="right" style="margin-left:10px" width="360" !bgcolor=#e7dcc3 colspan=2\|Bitruncated tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2\|(No image)
bgcolor=#e7dcc3\|Type	Uniform 4-honeycomb
bgcolor=#e7dcc3\|Schläfli symbol	t_1,2{4,3,3,4} or 2t{4,3,3,4} t_1,2{4,3^1,1} or 2t{4,3^1,1} t_2,3{4,3^1,1} q₂{4,3,3,3,4}
bgcolor=#e7dcc3\|Coxeter-Dynkin diagram	{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|4\|node}} {{CDD\|node\|4\|node_1\|3\|node_1\|split1\|nodes}} {{CDD\|nodes_11\|split2\|node_1\|3\|node\|4\|node}} {{CDD\|nodes_10ru\|split2\|node_1\|split1\|nodes_10lu}} = {{CDD\|node_1\|split1\|nodes\|4a4b\|nodes_h1h1}}
bgcolor=#e7dcc3\|4-face type	Bitruncated tesseract 40px Truncated 16-cell 40px
bgcolor=#e7dcc3\|Cell type	Octahedron 20px Truncated tetrahedron 20px Truncated octahedron 20px
bgcolor=#e7dcc3\|Face type	{3}, {4}, {6}
bgcolor=#e7dcc3\|Vertex figure	80px Square-pyramidal pyramid
bgcolor=#e7dcc3\|Coxeter group	${\tilde{C}}_4$ = [4,3,3,4] ${\tilde{B}}_4$ = [4,3^1,1] ${\tilde{D}}_4$ = [3^1,1,1,1]
bgcolor=#e7dcc3\|Dual
bgcolor=#e7dcc3\|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

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}} [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)
{{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations#4D}} x3x3x *b3o *b3o, x3x3x *b3o4o, o3x3o *b3x4o, o4x3x3o4o - batitit - O92
{{cite book |author=Conway JH, Sloane NJH |year=1998 |title=Sphere Packings, Lattices and Groups |publisher=Springer |edition=3rd |isbn=0-387-98585-9 |url-access=registration |url=https://archive.org/details/spherepackingsla0000conw_b8u0 }}

class="wikitable" align="right" style="margin-left:10px" width="360" !bgcolor=#e7dcc3 colspan=2\|Bitruncated tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2\|(No image)
bgcolor=#e7dcc3\|Type	Uniform 4-honeycomb
bgcolor=#e7dcc3\|Schläfli symbol	t_1,2{4,3,3,4} or 2t{4,3,3,4} t_1,2{4,3^1,1} or 2t{4,3^1,1} t_2,3{4,3^1,1} q₂{4,3,3,3,4}
bgcolor=#e7dcc3\|Coxeter-Dynkin diagram	{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|4\|node}} {{CDD\|node\|4\|node_1\|3\|node_1\|split1\|nodes}} {{CDD\|nodes_11\|split2\|node_1\|3\|node\|4\|node}} {{CDD\|nodes_10ru\|split2\|node_1\|split1\|nodes_10lu}} = {{CDD\|node_1\|split1\|nodes\|4a4b\|nodes_h1h1}}
bgcolor=#e7dcc3\|4-face type	Bitruncated tesseract 40px Truncated 16-cell 40px
bgcolor=#e7dcc3\|Cell type	Octahedron 20px Truncated tetrahedron 20px Truncated octahedron 20px
bgcolor=#e7dcc3\|Face type	{3}, {4}, {6}
bgcolor=#e7dcc3\|Vertex figure	80px Square-pyramidal pyramid
bgcolor=#e7dcc3\|Coxeter group	${\tilde{C}}_4$ = [4,3,3,4] ${\tilde{B}}_4$ = [4,3^1,1] ${\tilde{D}}_4$ = [3^1,1,1,1]
bgcolor=#e7dcc3\|Dual
bgcolor=#e7dcc3\|Properties	vertex-transitive