Explore the fascinating world of Platonic solids' symmetry in this 31-minute video lecture. Delve into the concept of rigid motions, focusing on rotations about fixed axes. Learn about angle normalization, where one full turn equals one, and discover the connection between the number of rigid motions and directed edges. Examine the rotational symmetries of various Platonic solids, including the tetrahedron, cube, and dodecahedron. Understand the role of duality in symmetries, particularly how the cube and octahedron, as well as the dodecahedron and icosahedron, share similar symmetrical properties. Gain insights into 3D rotations, directed edges, and the unique symmetrical characteristics of each Platonic solid in this comprehensive exploration of geometric symmetry.