|
ht0,3 hh |- |bgcolor=#e7dcc3|Coxeter diagrams|| or or = = |- |bgcolor=#e7dcc3|Cell types||, |- |bgcolor=#e7dcc3|Face types||triangle |- |bgcolor=#e7dcc3|Edge figure||()2 (rectangle) |- |bgcolor=#e7dcc3|Vertex figure||80px 80px80px (cuboctahedron) |- |bgcolor=#e7dcc3|Symmetry group||Fmm (225) |- |bgcolor=#e7dcc3|Symmetry||½, () The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway calls this honeycomb a tetroctahedrille, and its dual dodecahedrille. It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex. It is edge-transitive with 2 tetrahedra and 2 octahedra alternating on each edge. It is part of an infinite family of uniform honeycombs called alternated hypercubic honeycombs, formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets. It is also part of another infinite family of uniform honeycombs called simplectic honeycombs. In this case of 3-space, the cubic honeycomb is alternated, reducing the cubic cells to tetrahedra, and the deleted vertices create octahedral voids. As such it can be represented by an extended Schläfli symbol h as containing ''half'' the vertices of the cubic honeycomb. There's a similar honeycomb called gyrated tetrahedral-octahedral honeycomb which has layers rotated 60 degrees so half the edges have neighboring rather than alternating tetrahedra and octahedra. ==Cartesian coordinates== For an ''alternated cubic honeycomb'', with edges parallel to the axes and with an edge length of 1, the Cartesian coordinates of the vertices are: (For all integral values: ''i'',''j'',''k'' with ''i''+''j''+''k'' even) :(i, j, k) 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「Tetrahedral-octahedral honeycomb」の詳細全文を読む スポンサード リンク
|
