正多面体的数学和结晶学参数.doc

正多面体的数学和结晶学参数 Mathematic and Crystallographic Parameters of Regular Polyhedrons 正多面体名称 (Name of regular polyhedron) 正四面体(Regular tetrahedron) 正六面体(Regular hexahedron) 正八面体(Regular octahedron) 正十二面体 (Regular dodecahedron) 正二十面体 (Regular icosahedron) 图形符号 T O O I I 面形 正三角形 正方形 正三角形 正五边形 正三角形 正三面角 正三面角 直三面角 正四面角 正三面角 正五面角 面数? 4 6 8 12 20 棱数k 6 12 12 30 30 顶点数e 4 8 6 20 12 顶点到中心距离d 0.5443a 0.8660a 0.7071a 1.4103a 0.95105a ??? 棱长a (顶点到中心距离d) 1.8472 1.1547 1.4142 0.7091 1.0515 表面积S多面体 1.7321a2 6a2 3.4641a2 20.6458a2 8.6603a2 体积V多面体 0.1179a3 a3 0.4714a3 7.6631a3 2.1817a3 外接球表面积S外接球 3.7229a2 9.4242a2 6.2831a2 24.9938a2 11.3662a2 外接球体积V外接球 1.2410a3 2.7205a3 1.4809a3 11.7496a3 3.6033a3 中心原子半径r 0.0443a 0.3660a 0.2071a 0.9103a 0.45105a 配位原子半径R 0.5a 0.5a 0.5a 0.5a 0.5a r/R 0.0886 0.7320 0.4142 1.8206 0.9021 R/r 11.2867 1.3661 2.4142 0.5493 1.1085 点群符号 m3m m3m 对称要素 相邻对称轴之间的夹角 ∧ = 90° ∧ = 90° ∧ = 90° ∧ = 63.43° ∧ = 63.43° ∧ = 70.53° ∧ = 70.53° ∧ = 70.53° ∧ = 41.81° ∧ = 41.81° ∧ = 19.47° ∧ = 28.97° ∧ = 28.97° ∧ = 36° ∧ = 36° - ∧ = 19.47° ∧ = 19.47° ∧ = 37.38° ∧ = 37.38° - ∧ = 45° ∧ = 45° ∧ = 31.72° ∧ = 31.72° - ∧ = 34.88° ∧ = 34.88° ∧ = 20.90° ∧ = 20.90°