Regular dodecahedron a dodecahedron. Regular dodecahedron A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals). It is represented by the Schläfli symbol {5,3}. If the edge length of a regular dodecahedron is "a", the radius of a circumscribed sphere (one that touches the regular dodecahedron at all vertices) is and the radius of an inscribed sphere (tangent to each of the
Bilinski dodecahedron each containing "m" coparallel congruent edges. The Bilinski dodecahedron has 4 belts of 6 coparallel edges. These zonohedra are projection envelopes of the hypercubes, with n-dimensional projection basis, with golden ratio, φ. The specific basis for n=6 is: For n=5 the basis is the same with the 6th column removed, and for n=4 the 5th and 6th column are removed. 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