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
Dodecahedron pentagons around the sides which alternate upwards and downwards. This form has a hexagonal cross-section and identical copies can be connected as a partial hexagonal honeycomb, but all vertices will not match. The "rhombic dodecahedron" is a zonohedron with twelve rhombic faces and octahedral symmetry. It is dual to the quasiregular cuboctahedron (an Archimedean solid) and occurs in nature as a crystal form. The rhombic dodecahedron packs together to fill space. The "rhombic dodecahedron" can be seen as a degenerate pyritohedron where the 6 special edges have been reduced to zero length, reducing the pentagons into rhombic faces. The rhombic