Lecture: Polyhedra in everyday life and science

The polyhedra form a group of five geometric solids that have already been fully described by Plato. The solids in question are 4-, 6-, 8-, 12- and 20-sided polyhedra, formed from surfaces (triangles, squares or pentagons) with edges of equal length. In historical everyday life, the product of the craftsman and artist stands in contrast to the seemingly hermetic mathematical description. Historically, it was only they who succeeded in creating the amazing depiction of polyhedra and the shapes derived from them. They often used paper or spatial models for this purpose. They proceeded according to their own principles and in intensive examination of the material properties. Only ivory is capable of achieving the greatest fineness of form and new printing techniques replace outdated representations. Knowledge of polygraphs developed only very gradually in a field of tension between mathematicians and craftsmen. Even as late as the 19th century, some Euclid editions still show skewed and abstract diagrams and speak in an elitist, non-descriptive manner. On the other hand, there is a practical use for the polyhedron in everyday craftsmanship - quasi spontaneously - for example in jewelry, parlour games, architecture and lighting. The assumption that polyhedra have a mystical power also fires the imagination and commissions are issued for their research with the participation of important artists. In addition to anonymous men and women, well-known personalities such as Plato, Euclid, Jamnitzer, Ucello, Paccioli and Leonardo da Vinci, Dürer, Kepler, Brückner and Graham Bell took part in the research and depiction of the polyhedron.

The Dutch author, Prof. Dr.-Ing. Jos Tomlow, has been researching complex geometric phenomena for 50 years, particularly in connection with the history of construction, and has been teaching the basics of design and monument preservation at the Zittau/Görlitz University of Applied Sciences since 1995