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 The following points are vertices of a tetartoid pentagon under tetrahedral symmetry: under the following conditions: It can be seen as a tetrahedron, with edges divided into 3 segments, along with a center point of each triangular face. In Conway polyhedron notation it can be seen as gT, a gyro tetrahedron. A lower symmetry form of the regular dodecahedron can be constructed as the dual of a polyhedra constructed from two triangular anticupola connected base-to-base, called a "triangular gyrobianticupola." It has D symmetry, order 12. It has 2 sets of 3 identical pentagons on the top and bottom, connected 6