Construction of Three-Dimensional Model of Platonic Solid Coloring Mode Based on Group Theory
基于群论的柏拉图立体着色方案三维模型构造

An idea of implementing three-dimensional model for coloring mode of Platonic solids in accordance with space rotational group of Platonic solids is raised, and the problem in constructing three-dimensional model directly related to symmetry is thus resolved. A new classification method of group elements in a rotational group of Platonic solids is given. Three new concepts such as abstracted symmetry of group elements, local number of colors and saturated number of colors are put forward. Constructing coloring mode for the abstracted object and then constructing a method that the abstracted coloring mode is mapped into a three-dimensional space are raised. An algorithm for implementing this method is developed, and the algorithm and the three-dimensional model are visualized by means of Visual C++6.0 and Direct 3D. The results validate both the method put forward in this paper and the correctness of the algorithm.