Abstract: Equivariant mapping method is not only difficult to be implemented, but also constrained by the order of symmetry group. Drawn on the experience of the invariant theory of finite reflection group, this paper proposes an invariant mapping method to yield aesthetical spherical patterns and establishes a method to create infinite spherical patterns automatically. This method not only is easy to be implemented, but also can be extended to deal with the cases in the higher dimensional spaces.

Key words: finite reflection group, regular solids, invariant theory, invariant mapping

摘要： 等变映射方法在生成艺术图案中具有构造困难，受对称群阶数瓶颈限制等缺点。借鉴有限反射群不变论的结论，提出不变映射方法生成具有正多面体反射群对称性的球面艺术图案，建立了一种可生成无穷无尽球面图案的自动化方法。该方法不仅实施容易，且可类似地推广到高维空间中。

关键词: 有限反射群, 正多面体, 不变论, 不变映射