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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 Triangular hebesphenorotunda ： ウィキペディア英語版 Triangular hebesphenorotunda In geometry, the triangular hebesphenorotunda is one of the Johnson solids (''J''92). It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. However, it does have a strong relationship to the icosidodecahedron, an Archimedean solid. Most evident is the cluster of three pentagons and four triangles on one side of the solid. If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron. The triangular hebesphenorotunda is the only Johnson solid with faces of 3, 4, 5 and 6 sides. The 92 Johnson solids were named and described by Norman Johnson in 1966. ==Coordinates== The coordinates of the triangular hebesphenorotunda are: * The triangle opposite the hexagon: ::$\backslash left(0,\backslash \; \backslash frac,\backslash \; \backslash frac\backslash right)$, $\backslash left(\backslash pm1,\backslash \; -\backslash frac,\backslash \; \backslash frac\backslash right)$ * The bases of the triangles surrounding the previous triangle: ::$\backslash left(\backslash pm1,\backslash \; \backslash frac,\backslash \; \backslash frac\backslash right)$, $\backslash left(\backslash pm\backslash phi^2,\backslash \; -\backslash frac,\backslash \; \backslash frac\backslash right)$, $\backslash left(\backslash pm\backslash phi,\backslash \; -\backslash frac,\backslash \; \backslash frac\backslash right)$ * The tips of the pentagons opposite the first triangle: ::$\backslash left(\backslash pm\backslash phi^2,\backslash \; \backslash frac,\backslash \; \backslash frac\backslash right)$, $\backslash left(0,\backslash \; -\backslash frac,\backslash \; \backslash frac\backslash right)$ * The hexagon: ::$\backslash left(\backslash pm1,\backslash \; \backslash pm\backslash sqrt3,\backslash \; 0\backslash right)$, $\backslash left(\backslash pm2,\backslash \; 0,\backslash \; 0\backslash right)$ where $\backslash phi=\backslash frac$ is the Golden Ratio. These coordinates produce a triangular hebesphenorotunda with edge length 2, resting on the XY plane and having its 3-fold axis of symmetry aligned to the Z-axis. A second, inverted, triangular hebesphenorotunda can be obtained by negating the second and third coordinates of each point. This second polyhedron will be joined to the first at their common hexagonal face, and the pair will inscribe an icosidodecahedron. If the hexagonal face is scaled by the Golden Ratio, then the convex hull of the result will be the entire icosidodecahedron. 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「Triangular hebesphenorotunda」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.