After Euclid (end IV, beginning lll century B.C.). the theory of the regular polyhedrons obtained other important results through Appollonius(200 B.C.) and especially Ipsicle who produced a treatise found among the books of Euclid as the XIV book of the Elements. Several centuries after Christ another compiler, perhaps a disciple of Isidoro of Mileto, gathered other theorems on the regular polyhedrons, and added it as book XV to the Elements of Euclid.

Archimedes a Greek Scientist and Philosopher (287-212 B.C.) wrote numerous works one of which is entirely dedicated to polyhedrons: Investigations of Polyhedrons. This work is noted by an annotation of a manuscript of Pappus of Alessandria, from the third century A.D. (Pappus enunciated numerous geometric theorems). The Pappas manuscript is conserved in the Vatican library archives. Archimedes's work, like that of Plato , was subsequently lost.

It is reasonable to assume as some authors do, that the documentation arrived in Europe via Islamic civilisation and ancient Rome. In the Middle Ages Abu'l Wafa(940-998) continued the research following in the footsteps of Pappus. Averroè (1126-1198) who became an important author in European universities should also be remembered in this context.

In the Reneissance mathematicians and artists once more turned their attention to regular polyhedrons. The Florentine mathematician Lorenzo Sirigatti in "the Practice of Prespective" produced beautiful images of polyhedral spheres showed the complicated prototypes of Paolo Uccello, a club with an ashlar of quadrilateral pyramids.