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
Snub dodecahedron of snubbed polyhedra and tilings with vertex figure (3.3.3.3."n") and Coxeter–Dynkin diagram . These figures and their duals have ("n"32) rotational symmetry, being in the Euclidean plane for "n" = 6, and hyperbolic plane for any higher "n". The series can be considered to begin with "n" = 2, with one set of faces degenerated into digons. In the mathematical field of graph theory, a snub dodecahedral graph is the graph of vertices and edges of the snub dodecahedron, one of the Archimedean solids. It has 60 vertices and 150 edges, and is an Archimedean graph. Snub dodecahedron In geometry,