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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hexagonal tiling honeycomb ： ウィキペディア英語版 Hexagonal tiling honeycomb 2t 2t tr |- |bgcolor=#e7dcc3|Coxeter diagrams|| ↔ ↔ ↔ ↔ |- |bgcolor=#e7dcc3|Cells|| 80px |- |bgcolor=#e7dcc3|Faces||Hexagon |- |bgcolor=#e7dcc3|Edge figure||Triangle |- |bgcolor=#e7dcc3|Vertex figure||80px tetrahedron |- |bgcolor=#e7dcc3|Dual|| |- |bgcolor=#e7dcc3|Coxeter groups||$\}\_3$, () $\}\_3$, $$ In the field of hyperbolic geometry, the 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 three such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the tetrahedron is , the vertex figure of this honeycomb is an tetrahedron. Thus, six hexagonal tilings meet at each vertex of this honeycomb, and four edges meet at each vertex.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 ==Images== 320px Viewed in perspective outside of a Poincaré disk model, this shows one hexagonal tiling cell within the honeycomb, and its mid-radius horosphere (the horosphere incident with edge midpoints). In this projection, the hexagons grow infinitely small towards the infinite boundary asymptoting towards a single ideal point. It can be seen as similar to the order-3 apeirogonal tiling, of H2, with horocycle circumscribing vertices of apeirogonal faces. |- |240px |240px |- align=center |One hexagonal tiling of this honeycomb |order-3 apeirogonal tiling with a green apeirogon and its horocycle |} 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「Hexagonal tiling honeycomb」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.