Bitruncated cubic honeycomb

The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra (or, equivalently, bitruncated cubes). It has 4 truncated octahedra around each vertex. Being composed entirely of truncated octahedra, it is cell-transitive. It is also edge-transitive, with 2 hexagons and one square on each edge, and vertex-transitive. It is one of 28 uniform honeycombs.

Bitruncated cubic honeycomb
Type	Uniform honeycomb
Schläfli symbol	2t{4,3,4} t1,2{4,3,4}
Coxeter-Dynkin diagram
Cell type	(4.6.6)
Face types	square {4} hexagon {6}
Edge figure	isosceles triangle {3}
Vertex figure	(tetragonal disphenoid)
Space group Fibrifold notation Coxeter notation	Im3m (229) 8o:2 [[4,3,4]]
Coxeter group	${\displaystyle {\tilde {C}}_{3}}$, [4,3,4]
Dual	Oblate tetrahedrille Disphenoid tetrahedral honeycomb Cell:
Properties	isogonal, isotoxal, isochoric

John Horton Conway calls this honeycomb a truncated octahedrille in his Architectonic and catoptric tessellation list, with its dual called an oblate tetrahedrille, also called a disphenoid tetrahedral honeycomb. Although a regular tetrahedron can not tessellate space alone, this dual has identical disphenoid tetrahedron cells with isosceles triangle faces.