Origami: Platonic

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 C20 which is the smallest possible fullerene has been described experimentally in the 2000 year.

The corresponding hydrocarbon is the dodecahedrane, C20H20. 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).