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
Truncated trapezohedron Truncated trapezohedron An "n"-gonal truncated trapezohedron is a polyhedron formed by a "n"-gonal trapezohedron with "n"-gonal pyramids truncated from its two polar axis vertices. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism. The vertices exist as 4 "n"-gons in four parallel planes, with alternating orientation in the middle creating the pentagons. The regular dodecahedron is the most common polyhedron in this class, being a platonic solid, with 12 congruent pentagonal faces. A "truncated trapezohedron" has all vertices with 3 faces. This means that the dual polyhedra, the set of gyroelongated dipyramids, have all triangular faces.