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In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol , or sometimes by its vertex figure as 3.3.3.3.3 or 35. It is the dual of the dodecahedron, which is represented by , having three pentagonal faces around each vertex. A regular icosahedron is a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of six orientations. The name comes . The plural can be either "icosahedrons" or "icosahedra" (-). ==Dimensions== If the edge length of a regular icosahedron is ''a'', the radius of a circumscribed sphere (one that touches the icosahedron at all vertices) is : and the radius of an inscribed sphere (tangent to each of the icosahedron's faces) is : while the midradius, which touches the middle of each edge, is : where ''φ'' (also called ''τ'') is the golden ratio. 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「regular icosahedron」の詳細全文を読む スポンサード リンク
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