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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 Regular dodecahedron ： ウィキペディア英語版 Regular dodecahedron A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular composed of twelve regular pentagonal faces, with three meeting at each vertex, and is represented by the Schläfli symbol . It is one of the five Platonic solids. It has 20 vertices, 30 edges and 160 diagonals (60 face diagonals, 100 space diagonals).〔.〕 ==Dimensions== If the edge length of a regular dodecahedron is ''a'', the radius of a circumscribed sphere (one that touches the regular dodecahedron at all vertices) is :$r\_u\; =\; a\backslash frac\; \backslash left(1\; +\; \backslash sqrt\backslash right)\; \backslash approx\; 1.401258538\; \backslash cdot\; a$ and the radius of an inscribed sphere (tangent to each of the regular dodecahedron's faces) is :$r\_i\; =\; a\backslash frac\; \backslash sqrt\; +\backslash frac\backslash sqrt\}\; \backslash approx\; 1.113516364\; \backslash cdot\; a$ while the midradius, which touches the middle of each edge, is :$r\_m\; =\; a\backslash frac\; \backslash left(3\; +\backslash sqrt\backslash right)\; \backslash approx\; 1.309016994\; \backslash cdot\; a$ These quantities may also be expressed as :$r\_u\; =\; a\backslash ,\; \backslash frac\; \backslash phi$ :$r\_i\; =\; a\backslash ,\; \backslash frac$ where ''φ'' is the golden ratio. Note that, given a regular dodecahedron of edge length one, ''ru'' is the radius of a circumscribing sphere about a cube of edge length ''φ'', and ''ri'' is the apothem of a regular pentagon of edge length ''φ''. 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 dodecahedron」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.