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|- |bgcolor=#e7dcc3|Coxeter diagram|| ↔ ↔ |- |bgcolor=#e7dcc3|Cells|| 40px |- |bgcolor=#e7dcc3|Faces||hexagon |- |bgcolor=#e7dcc3|Edge figure||hexagon |- |bgcolor=#e7dcc3|Vertex figure|| or 40px 40px |- |bgcolor=#e7dcc3|Dual||Self-dual |- |bgcolor=#e7dcc3|Coxeter group||3, () 3, |- |bgcolor=#e7dcc3|Properties||Regular, quasiregular |} In the field of hyperbolic geometry, the order-6 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 hexagonal tiling honeycomb is . Since that of the hexagonal tiling of the plane is , this honeycomb has six such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the triangular tiling is , the vertex figure of this honeycomb is a triangular tiling. Thus, infinitely many hexagonal tilings meet at each vertex of this honeycomb.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 == Images== It is analogous to the 2D hyperbolic infinite-order apeirogonal tiling, with infinite apeirogonal faces and with all vertices are on the ideal surface. : 240px This honeycomb contains , that tile 2-hypercycle surfaces, similar to thes paracompact tilings, , : : 120px 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-6 hexagonal tiling honeycomb」の詳細全文を読む スポンサード リンク
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