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↔ |- |bgcolor=#e7dcc3|Coxeter diagrams|| ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ |- |bgcolor=#e7dcc3|Cells|| 40px 40px 40px 40px |- |bgcolor=#e7dcc3|Faces||Square |- |bgcolor=#e7dcc3|Edge figure||Square |- |bgcolor=#e7dcc3|Vertex figure||Square tiling, 40px 40px 40px 40px |- |bgcolor=#e7dcc3|Dual||Self-dual |- |bgcolor=#e7dcc3|Coxeter groups||() () |- |bgcolor=#e7dcc3|Properties||Regular, quasiregular |} In the geometry of hyperbolic 3-space, the order-4 square tiling honeycomb, is one of 11 paracompact regular honeycombs. It is called ''paracompact'' because it has infinite cells and vertex figures, with all vertices as ideal points at infinity. Given by Schläfli symbol , has four square tilings, around each edge, and infinite square tilings around each vertex in an square tiling vertex arrangement.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 == Symmetry== It has many reflective symmetry constructions, as a regular honeycomb, ↔ with alternate types (colors) of square tilings, and with 3 types (colors) of square tilings, with a ratio of 2:1:1. Two more half symmetry construction with pyramidal domains have () symmetry: ↔ , and ↔ . There are two high index subgroups, both index 8: () ↔ () exists with a pyramidal fundamental domain, () or , and secondly (), with 4 orthogonal sets of ultraparallel mirrors in an octahedral fundamental domain: . 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 square tiling honeycomb」の詳細全文を読む スポンサード リンク
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