The bitruncated cubic honeycomb shown here in relation to a 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.
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.
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The cubichoneycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells...
belong to 4 cells. The tetrahedral disphenoid honeycomb is the dual of the uniform bitruncatedcubichoneycomb. Its vertices form the A* 3 / D* 3 lattice...
The quarter cubichoneycomb, quarter cubic cellulation or bitruncated alternated cubichoneycomb is a space-filling tessellation (or honeycomb) in Euclidean...
cells. Twenty-eight such honeycombs are known: the familiar cubichoneycomb and 7 truncations thereof; the alternated cubichoneycomb and 4 truncations thereof;...
three different convex uniform honeycombs (space-filling tessellations): The cell-transitive bitruncatedcubichoneycomb can also be seen as the Voronoi...
the case p = 4, all cells are cubes and the result is the order-5 cubichoneycomb. Another two known ones are related to noncompact families. The tessellation...
3-polytopes), a bitruncated form is the truncated dual. For example, a bitruncated cube is a truncated octahedron. For a regular 4-polytope, a bitruncated form is...
1887, Lord Kelvin proposed a packing using only one solid, the bitruncatedcubichoneycomb with very slightly curved faces. In 1993, Denis Weaire and Robert...
as the cantitruncated order-4 square tiling honeycomb, tr{4,4,4}, . The bitruncated square tiling honeycomb, 2t{4,4,3}, has truncated cube and truncated...
it is called a cyclotruncated 5-cell honeycomb, with Coxeter graph , with 5-cell, truncated 5-cell, and bitruncated 5-cell facets. In 5-dimensions it is...
to the face diagonals of a cube. It tiles space to form the bitruncatedcubichoneycomb. Any zonohedron whose faces have the same combinatorial structure...
volume as a foam in 1887; his solution uses just one solid, the bitruncatedcubichoneycomb with very slightly curved faces to meet Plateau's laws. No better...
cell-transitive hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb. The truncated icosahedron can be constructed from a regular...
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