Polyhedric figures, perhaps drawn by Leonardo Da Vinci , illustrated the " De Divina Proportione" by Luca Pacioli , in the XV century. Luca Pacioli reawakened interest in them , shortly after the great painter Piero della Francesca , his contemporary and countryman , who wrote an interesting treatise De corporibus regularibus, a treatise which remained as a manuscript and which Pacioli translated publishing it in his aforementioned work.

The five regular polyhedrons once again took on a cosmic role with Keppler (1571-1630), who,in one of his first works maintained that the relationship of the distances of the six known planets from the sun , could be determined according to the properties of the so-called Platonic bodies. The study of the regular polyhedrons thus became part of the history of mathematics and Keppler was credited with the discovery of the stellar dodecahedron. Indeed, a stellar dodecahedron mosaic exists in the floor of the basilica of Saint Mark in Venice, created in all probability by Paolo Uccello.

In 1752 Eulero established the fundamental relationship between the number of vertices ,corners, and faces of a polyhedron. Using the dodecahedron which is composed of twelve faces and twenty vertices as an example ,summing the number of vertices (20) and the faces (12) and subtracting two, one obtains the number of corners (30). Icosahedron: 12 vertices + 20 faces - 2 faces = 30 corners. Octahedron: 6 Vertices + 8 - 2 faces =12 corners. Hexahedron: 8 vertices +6-2 faces =12 corners. Tetrahedron: 4 vertices + 4 - 2 faces = 6 corners.

Shapes inspired by regular polyhedrons abound in modern art and design too, from the works of Escher through modular architecture to the objects of Munari.

Giuseppe Mencarini

Bibl. Annuario Est 1976, Mondadori -MI- / Diz. Enc. Utet 1970/ A. Marcolli, Teoria del campo 2