Archimedean synthesis and magic numbers: "Sizing" giant molybdenum-oxide-based molecular spheres of the Keplerate type

Pythagorean harmony can be found in the spherical polyoxometalate clusters described here (see illustration for an example of a structure), since there are interesting relationships between the so-called magic numbers (12, 32, 42, 72, 132) relevant for spherical viruses and the number of the building blocks in the cluster. The size of these Keplerate clusters can be tailored by varying the type of connections between the pentagons by means of different spacers