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§1.前言.我们都知道正多面体只有五种,即正4、6、8、12、20面体;每一种都是由若干个边数相同的正多边形构成,且围绕着每一顶点的正多边形个数也一致.例如正12面体,就是由12个正5边形构成,且围绕着每一顶点的5边形个数都是3. 所有这些正多面体都与(2维)球面同胚(homeomorphic),也就是说,它们都是球面的拓扑像.一般在证明正多面体只有五种时,事实上已先假定了它们是与球面同胚
§1. Preface. We all know that there are only five regular polyhedrons, namely positive 4, 6, 8, 12 and 20 facets; each is composed of a number of regular polygons with the same number of edges and surrounds each vertex. The number of regular polygons is also the same. For example, a positive tetrahedron is composed of 12 regular pentagons, and the number of pentagons surrounding each vertex is 3. All of these regular polyhedrons are the same as (2D) spheres. Homeomorphics, that is, they are all topological images of a sphere. In general, when it is proved that there are only five kinds of regular polyhedrons, they are actually assumed to be homeomorphic to a sphere.