The five platonic solids have been build.

The dodecahedron is a platonic solid formed by 12 pentagonal faces, 20 vertices and 30 edges, in agreement with the Euler's rule (number of vertices - edges + faces = 2).

The C_{20} which is the smallest possible fullerene has been described experimentally in the 2000 year.

The corresponding hydrocarbon is the dodecahedrane, C_{20}H_{20}. It was synthesised for the first time by Leo Paquette and co. in 1982.

We studied the structural and energetic properties of this compound and a number of aza derivatives (Theoretical studies of aza analogues of platonic hydrocarbons. : Part III. Dodecahedrane and its aza derivatives).