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正多面体的数学和结晶学参数MathematicMathematic andand CrystallographicCrystallographic ParametersParameters ofof RegularRegular PolyhedronsPolyhedrons正多面体的数学和结晶学参数正多面体的数学和结晶学参数MathematicMathematic andand CrystallographicCrystallographic ParametersParameters ofof RegularRegular PolyhedronsPolyhedrons正多面体名正多面体名称称(Name(Name ofof regularregular polyhedron)polyhedron)正四面体正四面体(Regular(Regular tetrahedtetrahedron)ron)正六面体正六面体(Regular(Regular hexahedrohexahedron)n)正八面体正八面体(Regular(Regular octahedrooctahedron)n)正十二面体正十二面体(Regular(Regular dodecahedrondodecahedron) )正二十面体正二十面体(Regular(Regular icosahedron)icosahedron)图形符号图形符号TOOII面形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正三面角直三面角正四面角正三面角正五面角面数面数 ƒ ƒ4681220棱数棱数k k612123030顶点数顶点数e e4862012顶点到中心顶点到中心距离距离d d0.5443a0.8660a0.7071a1.4103a0.95105a棱长棱长a ( (顶点到中心顶点到中心距离距离d d) )1.84721.15471.41420.70911.0515表面积表面积 S S多面多面体体1.7321a26a23.4641a220.6458a28.6603a2体积体积 V V多面体多面体0.1179a3a30.4714a37.6631a32.1817a3外接球表面外接球表面积积 S S外接球外接球3.7229a29.4242a26.2831a224.9938a211.3662a2外接球体积外接球体积V V外接球外接球1.2410a32.7205a31.4809a311.7496a33.6033a3中心原子半中心原子半径径r r0.0443a0.3660a0.2071a0.9103a0.45105a配位原子半配位原子半径径R R0.5a0.5a0.5a0.5a0.5ar r/ /R R0.08860.73200.41421.82060.9021R R/ /r r11.28671.36612.41420.54931.1085点群符号点群符号m3mm3m对称要素对称要素∧ = 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°相邻对称轴相邻对称轴之间的夹角之间的夹角-∧ = 34.88°∧ = 34.88°∧ = 20.90°∧ = 20.90°。