Dodecahedron dodecahedron has several stellations, the first of which is also a parallelohedral spacefiller. Another important rhombic dodecahedron, the Bilinski dodecahedron, has twelve faces congruent to those of the rhombic triacontahedron, i.e. the diagonals are in the ratio of the golden ratio. It is also a zonohedron and was described by Bilinski in 1960. This figure is another spacefiller, and can also occur in non-periodic spacefillings along with the rhombic triacontahedron, the rhombic icosahedron and rhombic hexahedra. There are 6,384,634 topologically distinct "convex" dodecahedra, excluding mirror images—the number of vertices ranges from 8 to 20. (Two polyhedra are "topologically distinct" if
Truncated trapezohedron For example, the icosahedron is the dual of the dodecahedron. <br> 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