An Exploration of Symmetry (Eligible for NTU Credit)

The course content is released in two week blocks and consists of approximately 1 hr of lectures and tutorials per week. There are specific windows for uploading homework and undertaking peer-to-peer marking. These are detailed in the downloadable course timetable.

Part I: Basic Concepts of Symmetry

• Week 1: ‘A World of Symmetry’ will refresh your intuitive appreciation of symmetry in furniture, botany and common objects and introduce the mathematics of point symmetry.
  
  
• Week 2: ‘Tiling and the Asymmetric Unit’ begins by examining tessellations in architecture that will illustrate key concepts in plane symmetry including the asymmetric unit.  ‘Chirality’ discusses this key concept in symmetry and its impact on drug design and delivery.

Part II: Plane (2D) and Space (3D) Symmetry

• Week 3: ‘Escher and Graphic Design’ introduces symmetry operations in 2 dimensions and the difference between ‘primitive’ and ‘centered’ unit cells are illustrated using the art of Escher. ‘Nets’ examines the role of symmetry in Islamic architecture and history in the context of regular networks.
  
  
• Week 4: ‘Space Symmetry’ expands the symmetry operations to include 3 dimensional motion.  The methodology for reading and using the symmetry diagrams of the 17 plane groups and 230 space groups is introduced.

Part III: Symmetry in Crystals

• Week 5: ‘Crystal Forms and the Beauty of Minerals’ looks the external shape of mineral crystals and we learn about crystal power by visiting a geomancer. The manner in which crystal faceting reflects the internal atomic arrangements is described. ‘Planes, Directions and Unit Cell’ introduces the mathematics for describing perfect crystal structures.
  
  
• Week 6: ‘Platonic Solids and Atomic Bonding’ shows that regular geometrical shapes can be derived from folding plane nets into polyhedra that often describe atomic clustering and also the appearance of defects or asymmetry that are important aesthetically and technologically.  A laboratory tour will show the experiments used to extract crystallographic information.

Part IV: Symmetry and Technology

• Week 7: ‘Tailoring Crystals for Technology’ brings together chemistry and crystallography, shows how they are inter-related, and how they are adapted to engineer designer technological materials.  A clean room fabrication facility provides real world context for exploiting chemically- and physically-driven symmetry.
  
  
• Week 8:  ‘Looking for Broken Symmetry - Atomic Scale Imaging’ looks beyond 3 dimensional symmetry to higher dimensional repetitions found in incommensurate crystal structures. ‘Deceptive Perception - Symmetry & Furniture Design’ returns to the everyday appearance of symmetry that can now be explored analytically.

At the conclusion of this study, you will possess the tools and the motivation to look at symmetry with even greater delight, wonder and appreciation!

• Tim White - School of Materials Science & Engineering
• - School of Materials Science & Engineering