Regular 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 regular dodecahedron's
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