Symmetry in Modern Geometry

This lecture covers the fundamental theorems of symmetry, including the classification of isometries, modern definitions of symmetry groups, and practical applications in mirror image production. It also explores the 7 types of friezes, cell structures, and motifs, extending to 17 types of planar tessellations. The study delves into the complexity of planar tessellations, their architectural significance, and their mathematical intricacies. The lecture further discusses the generation of reflections in space through composition of orthogonal reflection planes, emphasizing the importance of axial and point reflections. The instructor demonstrates the construction of reflections through inversion of distances and the synthesis of isometries in space, providing practical examples in computer-aided design.