There are few kinds of regular polyhedrons. There are countless polyhedrons, but there are only five regular polyhedrons: regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron and regular icosahedron. Among them, the regular tetrahedron has the least number of faces and the regular icosahedron has the most. The crystals of some chemical elements are regular polyhedrons, for example, the crystals of salt are regular hexahedrons and the crystals of alum are regular octahedrons.

The Pythagorean school in ancient Greece specially studied five kinds of small polyhedra, and brought the research results to the bratton school for teaching. Therefore, these five regular polyhedrons are also called bratton solids in western mathematics.

A polyhedron is a solid surrounded by four or more polygons. It has three related definitions. In the traditional sense, it is a three-dimensional polyhedron, but in the updated sense, it is a bounded or unbounded generalization of polyhedron in any dimension. A topological polyhedron can be obtained by further extending the latter. Geometry surrounded by several planar polygons is called polyhedron.

The polygon surrounding a polyhedron is called the face of the polyhedron. The common edge of two faces is called the edge of a polyhedron. The common vertex of several sides is called the vertex of a polyhedron. If any face of a polyhedron is stretched and all other faces are on the same side of this face, the polyhedron is called a convex polyhedron.

A polyhedron has at least four faces. Polyheds are divided into tetrahedrons, pentahedrons, hexahedrons and so on according to the number of faces. If the number of faces of a polyhedron is f, the number of vertices is v and the number of edges is e, then f, e and v satisfy the following relationship: F+V=E+2.