Regular dodecahedron an edge length of one unit has the properties: The "regular dodecahedron " has two special orthogonal projections, centered, on vertices and pentagonal faces, correspond to the A and H Coxeter planes. In perspective projection, viewed above a pentagonal face, the regular dodecahedron can be seen as a linear-edged Schlegel diagram, or stereographic projection as a spherical polyhedron. These projections are also used in showing the four-dimensional 120-cell, a regular 4-dimensional polytope, constructed from 120 dodecahedra, projecting it down to 3-dimensions. The regular dodecahedron can also be represented as a spherical tiling. The following Cartesian coordinates define the 20 vertices
Regular dodecahedron ratio rectangles of ratio ("ϕ" + 1) : 1 and "ϕ" : 1 also fit perfectly within a regular dodecahedron. In proportion to this golden rectangle, an enclosed cube's edge is "ϕ", when the long length of the rectangle is "ϕ" + 1 (or "ϕ") and the short length is 1 (the edge shared with the regular dodecahedron). In addition, the center of each face of the regular dodecahedron form three intersecting golden rectangles. It can be projected to 3D from the 6-dimensional 6-demicube using the same basis vectors that form the hull of the rhombic triacontahedron from the 6-cube.