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Icosahedral honeycomb : ウィキペディア英語版
Icosahedral honeycomb
40px
|-
|bgcolor=#e7dcc3|Faces||triangle
|-
|bgcolor=#e7dcc3|Vertex figure||
dodecahedron
|-
|bgcolor=#e7dcc3|Dual||Self-dual
|-
|bgcolor=#e7dcc3|Coxeter group||3, ()
|-
|bgcolor=#e7dcc3|Properties||Regular
|}
The icosahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol , there are three icosahedra surround each edge, and 12 icosahedra surround each vertex, in a regular dodecahedral vertex figure.
==Description==
The dihedral angle of a Euclidean icosahedron is 138.2°, so it is impossible to fit three icosahedra around an edge in Euclidean 3-space. However, in hyperbolic space, properly scaled icosahedra can have dihedral angles exactly 120 degrees, so three of these fit around an edge.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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