An Exploration of Symmetry (Eligible for NTU Credit)

32 h
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Course details


The course content isreleased in two week blocks and consists of approximately 1 hr oflectures and tutorials per week. There are specific windows for uploadinghomework 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 intuitiveappreciation of symmetry in furniture, botany and common objects and introducethe mathematics of point symmetry.

  • Week 2: ‘Tiling and the Asymmetric Unit’ begins by examining tessellationsin architecture that will illustrate key concepts in plane symmetry includingthe asymmetric unit.  ‘Chirality’ discusses this key concept in symmetry and its impact on drug designand delivery.

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

  • Week 3: ‘Escher and Graphic Design’ introduces symmetry operations in 2 dimensionsand the difference between ‘primitive’ and ‘centered’ unit cells are illustratedusing the art of Escher. ‘Nets’ examines the role of symmetry in Islamicarchitecture and history in the context of regular networks.

  • Week4: ‘Space Symmetry’ expands the symmetry operations to include 3 dimensionalmotion.  The methodology for reading andusing the symmetry diagrams of the 17 plane groups and 230 space groups isintroduced.

Part III: Symmetry in Crystals

  • Week 5: ‘Crystal Forms and the Beauty of Minerals’ looks the external shape ofmineral crystals and we learn about crystal power by visiting a geomancer. The manner in which crystal facetingreflects the internal atomic arrangements is described. ‘Planes, Directions and Unit Cell’ introduces the mathematicsfor 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 orasymmetry that are important aesthetically and technologically.  A laboratory tour will show the experimentsused to extract crystallographic information.

Part IV: Symmetry and Technology

  • Week 7: ‘Tailoring Crystals for Technology’ brings together chemistry andcrystallography, shows how they are inter-related, and how they are adapted toengineer designer technological materials. A clean room fabrication facility provides real world context forexploiting chemically- and physically-driven symmetry.

  • Week 8:  ‘Looking for Broken Symmetry - Atomic Scale Imaging’ looks beyond 3 dimensional symmetry to higher dimensionalrepetitions found in incommensurate crystal structures. ‘Deceptive Perception - Symmetry & Furniture Design’ returns to the everyday appearance of symmetry that can now beexplored analytically.

At the conclusion of this study, you willpossess the tools and the motivation to look at symmetry with even greaterdelight, wonder and appreciation!




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


Young and research-intensive, Nanyang Technological University (NTU Singapore) is ranked 13th globally. It is also placed 1st amongst the world’s best young universities. NTU has about 33,000 students in the colleges of engineering, science, business, education, humanities, arts, social sciences. Its medical school is set up jointly with Imperial College London. A melting pot of international award-winning scientists, young talents and eminent global partners, NTU is also home to several world-class research institutes that builds on its strengths in interdisciplinary research.


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