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
Pentakis dodecahedron buckminsterfullerene: each surface segment represents a carbon atom. Equivalently, a truncated icosahedron is a model of buckminsterfullerene, with each vertex representing a carbon atom. The "pentakis dodecahedron" is also a model of some icosahedrally symmetric viruses, such as Adeno-associated virus. These have 60 symmetry related capsid proteins, which combine to make the 60 symmetrical faces of a "pentakis dodecahedron". The pentakis dodecahedron has three symmetry positions, two on vertices, and one on a midedge: Pentakis dodecahedron In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of