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Construction of three-dimensional model of Platonic solid coloring mode based on group theory. (Chinese) Zbl 1107.68508
Summary: The implementation of a three-dimensional model for the coloring mode of Platonic solids in accordance with the space rotational group of Platonic solids is studied, and the problem of constructing a 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.
MSC:
68U05Computer graphics; computational geometry
68U10Image processing (computing aspects)
68T45Machine vision and scene understanding