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80px |- |bgcolor=#e7dcc3|Faces||hexagon |- |bgcolor=#e7dcc3|Edge figure||pentagon |- |bgcolor=#e7dcc3|Vertex figure|| |- |bgcolor=#e7dcc3|Dual||Order-6 dodecahedral honeycomb |- |bgcolor=#e7dcc3|Coxeter group||3, () |- |bgcolor=#e7dcc3|Properties||Regular |} In the field of hyperbolic geometry, the order-5 hexagonal tiling honeycomb arises one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is called paracompact because it has infinite cells. Each cell consists of a hexagonal tiling whose vertices lie on a horosphere: a flat plane in hyperbolic space that approaches a single ideal point at infinity. The Schläfli symbol of the order-5 hexagonal tiling honeycomb is . Since that of the hexagonal tiling of the plane is , this honeycomb has five such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the icosahedron is , the vertex figure of this honeycomb is an icosahedron. Thus, 20 hexagonal tilings meet at each vertex of this honeycomb.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 == Symmetry== A lower symmetry, (), index 120 construction exists with regular dodecahedral fundamental domains, and a icosahedral shaped Coxeter diagram with 6 axial infinite order (ultraparallel) branches. 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-5 hexagonal tiling honeycomb」の詳細全文を読む スポンサード リンク
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