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
Trapezo-rhombic dodecahedron optimal way to stack spheres. As the Voronoi cell of a regular space pattern, it is a plesiohedron. It is the polyhedral dual of the triangular orthobicupola. The "trapezo-rhombic dodecahedron" can be seen as an elongation of another dodecahedron, which can be called a rhombo-triangular dodecahedron, with 6 rhombi (or squares) and 6 triangles. It also has d symmetry and is space-filling. It has 21 edges and 11 vertices. With square faces it can be seen as a cube split across the 3-fold axis, separated with the two halves rotated 180 degrees, and filling the gaps with triangles. When used