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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 List of Taylor polyhedra ： ウィキペディア英語版 List of Taylor polyhedra The Taylor polyhedra are the vertex-transitive polyhedra that are not included in the standard list of uniform polyhedra because they include the cross polygon and its double faced natural truncation , used to form the family of cross polyhedra, analogous to the family of star polyhedra. They are all generated by the six missing Schwarz triangles with octahedral symmetry (4 2 4/2), (4/3 2 4/2), (3 3 4/2), (3/2 3 4/2), (3/2 3/2 4/2) and (4/2 4/2 4/2). As with many other polyhedra generated by consideration of Schwarz triangles, they are technically degenerate and have coincident vertices, faces or edges, those from the last four triangles listed being double versions of those in the first two triangles. These polyhedra generally have densities greater than 1, the tiling of the sphere that produces them taking place in multiple layers with several visits to any one vertex or edge. However they are best appreciated by accepting , the crossed digon, as a polygon in its own right. Although it has no area, it is self inverse and sits naturally between the usual polygons with positive area such as and their inverses with negative area such as . Taken with the accepted uniform polyhedra and the polyhedra generated by Schwarz triangles generally, the Taylor polyhedra allow a more complete classification to emerge, without the peculiar gaps that currently exist within the uniform polyhedra. == List == | () | 4/2.4/2.4/2.4/2 | 6 | 12 | 6×4/2 |- | Truncated great hexahedron | 4/2 2 |4 | t | () | 8.8.4/2 | 24 | 36 | 6×8 6×4/2 |- | Truncated stellated hexahedron (triple cube) | 4 2 |4/2 | t | () | 24.24.4 | 8×3 | 12×3 | 6×24 6×4 |- | Hexahexahedron | 2| 4 4/2 | $\backslash left\backslash \backslash right\backslash \}$ | () | 4.4/2.4.4/2 | 12 | 24 | 6×4 6×4/2 |- | Truncated hexahexahedron | 4 2 4/2| | t$\backslash left\backslash \backslash right\backslash \}$ | () | 8.24.4 | 24×2 | 24×2 24×1 | 6×8 6×24 12×4 |- | Rhombihexahexahedron | 4 4/2 |2 | r$\backslash left\backslash \backslash right\backslash \}$ | () | 4.4/2.4.4 | 24 | 48 | 6×4 6×4/2 12×4 |- | Snub hexahexahedron | |4 2 4/2 | s$\backslash left\backslash \backslash right\backslash \}$ | () | 3.4/2.3.3.4 | 24 | 60 | 6×4 6×4/2 24×3 |- | Quasitruncated great hexahedron | 4/2 2 |4/3 | t | () | 8/3.8/3.4/2 | 24 | 36 | 6×8/3 6×4/2 |- | Quasitruncated hexahexahedron | 4/3 2 4/2| | t$\backslash left\backslash \backslash right\backslash \}$ | () | 8/3.24.4 | 24×2 | 24×2 24×1 | 6×8/3 6×24 12×4 |- | Double stellated hexahedron | 4/2| 4/2 4/2 | | | (4/2.4/2.4/2.4/2)2 | 6×2 | 12×2 | 6×4/2 6×4/2 |- | Double hexahexahedron | 4/2 4/2 |4/2 | | | 4/2.24.4/2.24 | 12×2 | 24×2 | 6×4/2 6×4/2 6×24 |- | Double truncated stellated hexahedron (sixfold cube) | 4/2 4/2 4/2| | | | 24.24.24 | 8×6 | 12×6 | 6×24 6×24 6×24 |- | Triple stella octangula | |4/2 4/2 4/2 | | | 3.4/2.3.4/2.3.4/2 | 8×3 | 24×3 | 24×3 6×4/2 12×4/2 |- |} 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「List of Taylor polyhedra」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.