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|- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| |- |bgcolor=#e7dcc3|Cells|| 40px |- |bgcolor=#e7dcc3|Faces||pentagon |- |bgcolor=#e7dcc3|Vertex figure||100px |- |bgcolor=#e7dcc3|Dual||Self-dual |- |bgcolor=#e7dcc3|Coxeter group||3, [5,3,5] |- |bgcolor=#e7dcc3|Properties||Regular |} The order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol , it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is an icosahedron. == Description== The dihedral angle of a Euclidean regular dodecahedron is ~116.6°, so no more than three of them can fit around an edge in Euclidean 3-space. In hyperbolic space, however, the dihedral angle is smaller than it is in Euclidean space, and depends on the size of the figure; the smallest possible dihedral angle is 60°, for an ideal hyperbolic regular dodecahedron with infinitely long edges. The dodecahedra in this dodecahedral honeycomb are sized so that all of their dihedral angles are exactly 72°. 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 dodecahedral honeycomb」の詳細全文を読む スポンサード リンク
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