![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Bitruncated_cubic_tiling.png/640px-Bitruncated_cubic_tiling.png&w=640&q=50)
Bitruncated cubic honeycomb
From Wikipedia, the free encyclopedia
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 | |
Dual | Oblate tetrahedrille Disphenoid tetrahedral honeycomb Cell: ![]() |
Properties | isogonal, isotoxal, isochoric |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/76/Cubes-A4_ani.gif/220px-Cubes-A4_ani.gif)
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.