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
Diminished rhombic dodecahedron a cuboctahedron. It retains 5 square faces, and 4 equilateral triangle faces of the cuboctahedron. The 13 Cartesian coordinate can be positioned as: Augmenting two opposite squares will create a dihedral rhombic dodecahedron, doubling the symmetry to "D" symmetry, order 16. Augmenting pyramids on all six square faces, with merged faces will produce a regular octahedron, restoring full octahedral symmetry, order 48. Diminished rhombic dodecahedron In geometry, a diminished rhombic dodecahedron is a rhombic dodecahedron with one or more vertices removed. This article describes diminishing one 4-valence vertex. This diminishment creates one new square face while 4 rhombic faces are