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
Bilinski dodecahedron Bilinski dodecahedron In geometry, the Bilinski dodecahedron is a 12-sided convex polyhedron with congruent rhombic faces. It has the same topology but different geometry from the face transitive rhombic dodecahedron, another 12-sided polyhedron with congruent rhombic faces. This shape appears in a 1752 book by John Lodge Cowley, labeled as the dodecarhombus. It is named after Stanko Bilinski, who rediscovered it in 1960. Bilinski himself called it the rhombic dodecahedron of the second kind. Bilinski's discovery corrected a 75-year-old omission in Evgraf Fedorov's classification of convex polyhedra with congruent rhombic faces. In the rhombi of the Bilinski dodecahedron, the ratio