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
Tetrahedrally diminished dodecahedron triangles are always equilateral, while the quadrilaterals are irregular, although the two adjacent edges that meet at the vertices of a tetrahedron are equal. As a self-dual hexadecahedron, it is one of 302404 forms, 1476 with at least order 2 symmetry, and the only one with tetrahedral symmetry. As a diminished regular dodecahedron, with 4 vertices removed, the quadrilaterals faces are trapezoids. As a stellation of the regular icosahedron it is one of 32 stellations defined with tetrahedral symmetry. It has kite faces. In Conway polyhedron notation, it can represented as pT, applying George W. Hart's propeller operator to a