Lecture
This lecture provides the underlying reasoning for the parametric construction of exercise 6-EXa, where the use of symmetries sheds new light on the conclusion of Euclid's Elements. It delves into the historical background of symmetries, highlighting their significance in the context of regular polyhedra. The lecture explores the concept of commensurability and the evolution of the modern understanding of symmetry. Detailed examination of the symmetries of regular polyhedra is provided, focusing on rotations and their role in leaving a figure globally invariant. The lecture also discusses the number of symmetries of polyhedra, the relationship between the number of symmetries and the faces of the polyhedron, and the significance of angles in rotations.