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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 Table of polyhedron dihedral angles ： ウィキペディア英語版 Table of polyhedron dihedral angles The dihedral angles for the edge-transitive polyhedra are: | (4.4.4) | π/2 | 90° |- align="center" | | align="left" | Octahedron | | (3.3.3.3) | π − arccos(1/3) | 109.47° |- align="center" | | align="left" | Dodecahedron | | (5.5.5) | π − arctan(2) | 116.56° |- align="center" | | align="left" | Icosahedron | | (3.3.3.3.3) | π − arccos(√5/3) | 138.19° |-align="center" ! colspan=6 | Kepler-Poinsot solids (regular nonconvex) |- align="center" | | align="left" |Small stellated dodecahedron|| | (5/2.5/2.5/2.5/2.5/2) | π − arctan(2) | 116.56° |- align="center" | | align="left" |Great dodecahedron|| | (5.5.5.5.5)/2 | arctan(2) | 63.435° |- align="center" | | align="left" |Great stellated dodecahedron|| | (5/2.5/2.5/2) | arctan(2) | 63.435° |- align="center" | | align="left" |Great icosahedron|| | (3.3.3.3.3)/2 | arcsin(2/3) | 41.810° |- align="center" ! colspan=6 | Quasiregular polyhedra (Rectified regular) |- align="center" | | align="left" | Tetratetrahedron | r | (3.3.3.3) | $\backslash pi\; -\; \backslash arccos\; \backslash right)\}$ | 109.47° |- align="center" | | align="left" | Cuboctahedron | r | (3.4.3.4) | $\backslash pi\; -\; \backslash arccos\}\; \backslash right)\}$ | 125.264° |- align="center" | | align="left" | Icosidodecahedron | r | (3.5.3.5) | $\backslash pi\; -\; \backslash arccos\; \}\; \backslash right)\; \}$ | 142.623° |- align="center" | | align="left" | Dodecadodecahedron | r | (5.5/2.5.5/2) | π − arctan(2) | 116.56° |- align="center" | | align="left" | Great icosidodecahedron | r | (3.5/2.3.5/2) | | |- align="center" ! colspan=6 | Ditrigonal polyhedra |- align="center" | | align="left" | Small ditrigonal icosidodecahedron | a | (3.5/2.3.5/2.3.5/2) | | |- align="center" | | align="left" | Ditrigonal dodecadodecahedron | b | (5.5/3.5.5/3.5.5/3) | | |- align="center" | | align="left" | Great ditrigonal icosidodecahedron | c | (3.5.3.5.3.5)/2 | | |- align="center" ! colspan=6 | Hemipolyhedra |- align="center" | | align="left" | Tetrahemihexahedron | o | (3.4.3/2.4) | | 54.73° |- align="center" | | align="left" | Cubohemioctahedron | o | (4.6.4/3.6) | | 54.73° |- align="center" | | align="left" | Octahemioctahedron | o | (3.6.3/2.6) | | 70.53° |- align="center" | | align="left" | Small dodecahemidodecahedron | o | (5.10.5/4.10) | | 26.063° |- align="center" | | align="left" | Small icosihemidodecahedron | o | (3.10.3/2.10) | | 116.56° |- align="center" | | align="left" | Great dodecahemicosahedron | o | (5.6.5/4.6) | | |- align="center" | | align="left" | Small dodecahemicosahedron | o | (5/2.6.5/3.6) | | |- align="center" | | align="left" | Great icosihemidodecahedron | o | (3.10/3.3/2.10/3) | | |- align="center" | | align="left" | Great dodecahemidodecahedron | o | (5/2.10/3.5/3.10/3) | | |- align="center" ! colspan=6 | Quasiregular dual solids |- align="center" | | align="left" | Rhombic hexahedron (Dual of tetratetrahedron) | - | V(3.3.3.3) | π − π/2 | 90° |- align="center" | | align="left" | Rhombic dodecahedron (Dual of cuboctahedron) | - | V(3.4.3.4) | π − π/3 | 120° |- align="center" | | align="left" | Rhombic triacontahedron (Dual of icosidodecahedron) | - | V(3.5.3.5) | π − π/5 | 144° |- align="center" | | align="left" | Medial rhombic triacontahedron (Dual of dodecadodecahedron) | - | V(5.5/2.5.5/2) | π − π/3 | 120° |- align="center" | | align="left" | Great rhombic triacontahedron (Dual of great icosidodecahedron) | - | V(3.5/2.3.5/2) | π − π/(5/2) | 72° |- align="center" ! colspan=6 | Duals of the ditrigonal polyhedra |- align="center" | | align="left" | Small triambic icosahedron (Dual of small ditrigonal icosidodecahedron) | - | V(3.5/2.3.5/2.3.5/2) | | |- align="center" | | align="left" | Medial triambic icosahedron (Dual of ditrigonal dodecadodecahedron) | - | V(5.5/3.5.5/3.5.5/3) | | |- align="center" | | align="left" | Great triambic icosahedron (Dual of great ditrigonal icosidodecahedron) | - | V(3.5.3.5.3.5)/2 | | |- align="center" ! colspan=6 | Duals of the hemipolyhedra |- align="center" | | align="left" | Tetrahemihexacron (Dual of tetrahemihexahedron) | - | V(3.4.3/2.4) | π − π/2 | 90° |- align="center" | | align="left" | Hexahemioctacron (Dual of cubohemioctahedron) | - | V(4.6.4/3.6) | π − π/3 | 120° |- align="center" | | align="left" | Octahemioctacron (Dual of octahemioctahedron) | - | V(3.6.3/2.6) | π − π/3 | 120° |- align="center" | | align="left" | Small dodecahemidodecacron (Dual of small dodecahemidodecacron) | - | V(5.10.5/4.10) | π − π/5 | 144° |- align="center" | | align="left" | Small icosihemidodecacron (Dual of small icosihemidodecacron) | - | V(3.10.3/2.10) | π − π/5 | 144° |- align="center" | | align="left" | Great dodecahemicosacron (Dual of great dodecahemicosahedron) | - | V(5.6.5/4.6) | π − π/3 | 120° |- align="center" | | align="left" | Small dodecahemicosacron (Dual of small dodecahemicosahedron) | - | V(5/2.6.5/3.6) | π − π/3 | 120° |- align="center" | | align="left" | Great icosihemidodecacron (Dual of great icosihemidodecacron) | - | V(3.10/3.3/2.10/3) | π − π/(5/2) | 72° |- align="center" | | align="left" | Great dodecahemidodecacron (Dual of great dodecahemidodecacron) | - | V(5/2.10/3.5/3.10/3) | π − π/(5/2) | 72° |} == References == * Coxeter, ''Regular Polytopes'' (1963), Macmillan Company * * ''Regular Polytopes'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 (Table I: Regular Polytopes, (i) The nine regular polyhedra in ordinary space) * (Section 3-7 to 3-9) * 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「Table of polyhedron dihedral angles」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. 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