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
Disdyakis dodecahedron be drawn in a number of symmetric orthogonal projective orientations. Between a polyhedron and its dual, vertices and faces are swapped in positions, and edges are perpendicular. The disdyakis dodecahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron. It is a polyhedra in a sequence defined by the face configuration V4.6.2"n". This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any "n" ≥ 7. With an