正十二面体的旋转群诱导出的置换群的轮换指标

Educed permutation group's rotation index from rotation group of regular dodecahedron

目的:给出正十二面体的旋转群所诱导出的置换群的轮换指标.方法:通过分析所诱导出的置换群中元素的置换类型,利用Burnside定理和Polya定理给出相应的轮换指标多项式.结果:给出了所诱导出的6种置换群的循环指标多项式.结论:所给出的循环指标多项式可以为正十二面体的着色计数问题提供计算依据.

Objective：To give the permutation group＇s rotation index of rotation group of regular dodecahedron. Methods：To take Burnside theorem and Polya theorem as means.Result Conclusion：To present six turn-take index polynomials which are helpful to determine the vertex-coloring formulas of regular dodecahedron.