How to make the right dodecahedron

A dodecahedron is a regular polyhedron whose faces are twelve regular pentagons. The simplest polyhedron to be constructed is the hexahedron or cube; all other polyhedrons can be constructed by writing or describing them near it. The dodecahedron can be constructed by describing it near the cube.

Instruction manual

one

Build a cube with edge length a. Calculate the length of the dodecahedron under construction using the formula: m = -a / 2 + av5 / 2, where a is the length of the cube edge.

2

On the edge of the SPRQ, draw a line K1L1 connecting the midpoints of the ribs. On this line, set aside a segment of length m that is equally spaced from the edges of the cube. Draw the perpendiculars through the ends of the line to the SPRQ face.

3

Construct the pentagon ABCDE with the diagonals AC and BE. AB = BC = a. Calculate the height of triangle ABC and designate it s = BN.

4

On the perpendiculars, find the points whose distance from the midpoints of the edges is s, i.e. LL1 = KK1 = s. Connect the now found points to the vertices of the cube.

5

Repeat constructions 2 and 4 for each face, as a result you get the correct polyhedron described near the cube - the dodecahedron.