For two millennia, the regular Platonic polyhedra have fascinated not just mathematicians,  but also artists and a good fraction of the general public. When realized in appropriate materials, these shapes yield beautiful art objects. In a more abstract way, they demonstrate intriguing geometrical relationships, particularly when the general idea underlying these objects is extended to higher dimensions.

In this seminar, Hans Schepker will present some of his beautiful constructions  realized in glass and metal and tell the audience how he conceives of these shapes and then realizes these artful sculptures. Carlo Sequin will analyze why there are exactly five Platonic solids, and then use these insights to derive the number of completely regular polytopes in 4 and higher dimensions.