Regular dodecahedron whereas a regular icosahedron has 20 faces and 12 vertices. Both have 30 edges. A cube can be embedded within a regular dodecahedron, affixed to eight of its equidistant vertices, in five different positions. In fact, five cubes may overlap and interlock inside the regular dodecahedron to result in the compound of five cubes. The ratio of the edge of a regular dodecahedron to the edge of a cube embedded inside such a regular dodecahedron is 1 : "ϕ", or ("ϕ" − 1) : 1. The ratio of a regular dodecahedron's volume to the volume of a cube embedded inside
Bilinski dodecahedron Bilinski dodecahedron the shorter body diagonals of this type have no parallel face diagonals. The Bilinski dodecahedron can be formed from the rhombic triacontahedron (another zonohedron with 30 golden rhombic faces) by removing or collapsing two zones or belts of faces with parallel edges. Removing only one of these two zones produces, instead, the rhombic icosahedron, and removing three produces the golden rhombohedra. The Bilinski dodecahedron can be dissected into four golden rhombohedra, two of each type. The vertices of these zonohedra can be computed by linear combinations of 3 to 6 vectors. A belt m means "n" directional vectors,