边长和角分别都相 等的多边形叫正多边 形,正多边形有许多许 多种．形状大小完全一 样的正多边形围成的多 面体叫做正多面体．而 正多面体只有五种:如 图1,正四面体;如图 2,正六面体(正方体); 如图3,正八面体;如 图4,正十二面体;如 图5,正二十面体． 正多面体只有五 种!对此,许多同学感 到不可思议． 正多面体为什么只 有这五种呢? 弄清这个问题,需 要用到的数学知识有以 下三点: The polygons with equal lengths and angles are called positive polygons, and there are many regular polygons. A polyhedron surrounded by regular polygons of exactly the same size is called a regular polyhedron. However, there are only five polyhedrons: Figure 1, regular tetrahedron; Figure 2, regular hexahedron (cuboid); Figure 3, regular octahedron; as in Figure 4, regular dodecahedron; as in Figure 5, regular icosahedron. There are only five polyhedrons! For this, many students feel incredible. Why are there only five kinds of polyhedrons? To clarify this question, there are three things to use in mathematics: