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|- |bgcolor=#e7dcc3|Coxeter diagrams|| ↔ ↔ ↔ |- |bgcolor=#e7dcc3|Cells||octahedron |- |bgcolor=#e7dcc3|Faces||triangle |- |bgcolor=#e7dcc3|Edge figure||square |- |bgcolor=#e7dcc3|Vertex figure||square tiling, 40px 40px 40px 40px |- |bgcolor=#e7dcc3|Dual||Square tiling honeycomb, |- |bgcolor=#e7dcc3|Coxeter groups||() () |- |bgcolor=#e7dcc3|Properties||Regular |} In the geometry of hyperbolic 3-space, the order-4 octahedral honeycomb is a regular paracompact honeycomb. It is called ''paracompact'' because it has infinite vertex figures, with all vertices as ideal points at infinity. Given by Schläfli symbol , it has four octahedra, around each edge, and infinite octahedra around each vertex in an square tiling vertex arrangement.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 == Symmetry == A half symmetry construction, (), exists as , with alternating two types (colors) of octahedral cells. ↔ . A second half symmetry, (): ↔ . A higher index subsymmetry, (), index 8, exists with a pyramidal fundamental domain, (): . This honeycomb contains , that tile 2-hypercycle surfaces, similar to the paracompact tiling or : 120px 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「Order-4 octahedral honeycomb」の詳細全文を読む スポンサード リンク
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