Explore the fascinating world of "forbidden symmetry" in this Q&A session with renowned mathematician Sir Roger Penrose. Delve into the mathematical underpinnings of non-repeating patterns and their applications in design and architecture. Learn about crystallographic symmetries, Penrose tilings, and their use in architectural designs, including the unique tiling at the Oxford Mathematics Institute. Discover the connection between these patterns and quasi-crystalline materials in atomic structures, which led to a Nobel Prize in chemistry. Gain insights into topics such as tiling spheres, periodic tiling, mirror symmetry, infinite shapes, higher-dimensional tilings, quantum action, and the emergence of a new kind of science related to quasicrystals.