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
Rhombic dodecahedron The "rhombic dodecahedron" has four special orthogonal projections along its axes of symmetry, centered on a face, an edge, and the two types of vertex, threefold and fourfold. The last two correspond to the B and A Coxeter planes. The eight vertices where three faces meet at their obtuse angles have Cartesian coordinates: The coordinates of the six vertices where four faces meet at their acute angles are: The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates and with parameter "h" = 1. The "rhombic dodecahedron" is a parallelohedron, a space-filling