Regular polyhedron is called the convex polyhedron if all its sides represent equal among themselves, regular polygons, at the same time in each its top the identical number of edges meets. There are five regular polyhedrons – a tetrahedron, an octahedron, an icosahedron, a hexahedron (cube) and a dodecahedron. The icosahedron is a polyhedron which sides are twenty correct triangles equal among themselves.
Instruction
1. For creation of an icosahedron we will use creation of a cube. Let's designate one of its sides of SPRQ.
2. Carry out two pieces of AA1 and BB1 so that they connected the middle of edges of a cube, that is as = AP = A1R = A1Q = BS = BQ.
3. On pieces of AA1 and BB1 postpone equal between pieces CC1 and DD1 n length so that their ends were as equals distances from cube edges, i.e. BD = B1D1 = AC = A1C1.
4. Pieces of CC1 and DD1 are edges of an icosahedron under construction. Having constructed pieces of CD and C1D, you receive one of icosahedron sides – CC1D.
5. Repeat constructions 2, 3 and 4 for all sides of a cube - as a result receive the regular polyhedron entered in a cube – an icosahedron. By means of a hexahedron it is possible to construct any regular polyhedron.