Dodecahedron called regular polyhedron,whose faces are twelve regular pentagons. The simplest to construct regular polyhedron is a hexahedron or cube, all the other polyhedra can be constructed by inscribing or describing them about it.
The dodecahedron can be constructed, describing it around the cube.
Build a cube with edge length a. Calculate the length of the dodecahedron is being built by the formula: m = -a / 2 + av5 / 2, where a - the length of the cube edge.
On the verge of SPRQ K1L1 draw a line connecting the mid-ribs. On this line, set aside a segment of length m, equidistant from the edges of the cube. Through the end of the segment draw perpendiculars to the brink SPRQ.
Construct a pentagon ABCDE with diagonals AC and BE. AB = BC = a. Calculate the height of the triangle ABC and mark it s = BN.
Get on the perpendicular point, the distance from which until the middle of the ribs is equal to s, ie LL1 = KK1 = s. Connect now the results point to the vertices of the cube.
Povtoroyte construction of 2 and 4 for each face, as a result you get a regular polyhedron circumscribed around the cube - dodecahedron.