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|- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| |- |bgcolor=#e7dcc3|Cell type||(''4.6.6'') |- |bgcolor=#e7dcc3|Face types||square hexagon |- |bgcolor=#e7dcc3|Edge figure||isosceles triangle |- |bgcolor=#e7dcc3|Vertex figure|| (tetragonal disphenoid) |- |bgcolor=#e7dcc3|Space group Fibrifold notation Coxeter notation|| 8o:2 |- |bgcolor=#e7dcc3|Dual||Oblate tetrahedrille Disphenoid tetrahedral honeycomb |- |bgcolor=#e7dcc3|Properties||isogonal, isotoxal, isochoric |} 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. == Geometry== It can be realized as the Voronoi tessellation of the body-centred cubic lattice. Lord Kelvin conjectured that a variant of the ''bitruncated cubic honeycomb'' (with curved faces and edges, but the same combinatorial structure) is the optimal soap bubble foam. However, the Weaire–Phelan structure is a less symmetrical, but more efficient, foam of soap bubbles. The honeycomb represents the permutohedron tessellation for 3-space. The coordinates of the vertices for one octahedron represent a hyperplane of integers in 4-space, specifically permutations of (1,2,3,4). The tessellation is formed by translated copies within the hyperplane. :240px The tessellation is the highest tessellation of parallelohedrons in 3-space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「bitruncated cubic honeycomb」の詳細全文を読む スポンサード リンク
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