Cantitruncated tesseractic honeycomb

{{Short description|Uniform space-filling tessellation in Euclidean 4-space}}

class="wikitable" align="right" style="margin-left:10px" width="360" !bgcolor=#e7dcc3 colspan=2\|Cantitruncated tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2\|(No image)
bgcolor=#e7dcc3\|Type	Uniform 4-honeycomb
bgcolor=#e7dcc3\|Schläfli symbol	tr{4,3,3,4} tr{4,3,3^1,1}
bgcolor=#e7dcc3\|Coxeter-Dynkin diagram	{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|4\|node}} {{CDD\|node_1\|4\|node_1\|3\|node_1\|split1\|nodes}}
bgcolor=#e7dcc3\|4-face type	t_0,1,2{4,3,3} 40px t_0,1{3,3,4} 40px {3,4}×{} 40px
bgcolor=#e7dcc3\|Cell type	Truncated cuboctahedron 20px Octahedron 20px Truncated tetrahedron 20px Triangular prism 20px
bgcolor=#e7dcc3\|Face type	{3}, {4}, {6}
bgcolor=#e7dcc3\|Vertex figure	Square double pyramid
bgcolor=#e7dcc3\|Coxeter group	${\tilde{C}}_4$ = [4,3,3,4] ${\tilde{B}}_4$ = [4,3,3^1,1]
bgcolor=#e7dcc3\|Dual
bgcolor=#e7dcc3\|Properties	vertex-transitive

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

Related 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, {{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}} o3x3o *b3x4x, x4x3x3o4o - grittit - O94
{{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\|Cantitruncated tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2\|(No image)
bgcolor=#e7dcc3\|Type	Uniform 4-honeycomb
bgcolor=#e7dcc3\|Schläfli symbol	tr{4,3,3,4} tr{4,3,3^1,1}
bgcolor=#e7dcc3\|Coxeter-Dynkin diagram	{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|4\|node}} {{CDD\|node_1\|4\|node_1\|3\|node_1\|split1\|nodes}}
bgcolor=#e7dcc3\|4-face type	t_0,1,2{4,3,3} 40px t_0,1{3,3,4} 40px {3,4}×{} 40px
bgcolor=#e7dcc3\|Cell type	Truncated cuboctahedron 20px Octahedron 20px Truncated tetrahedron 20px Triangular prism 20px
bgcolor=#e7dcc3\|Face type	{3}, {4}, {6}
bgcolor=#e7dcc3\|Vertex figure	Square double pyramid
bgcolor=#e7dcc3\|Coxeter group	${\tilde{C}}_4$ = [4,3,3,4] ${\tilde{B}}_4$ = [4,3,3^1,1]
bgcolor=#e7dcc3\|Dual
bgcolor=#e7dcc3\|Properties	vertex-transitive