Week1: What is symmetry? Bilateral and rotational symmetries of finite 2D objects.

2D symmetry in art, architectural facades, and in hub caps.

Week2: Symmetry by repetition. Linear frieze patterns. Basic symmetry operations

Week3: Rotational symmetries of finite objects; wrapping friezes around a solid.

Week4: Symmetries; the Platonic and Archimedean solids.

Week5: 4-dimensional, and higher-dimensional completely regular ("Platonic") solids.

Week6: Lattices, wallpaper patterns, 2D tilings.

Week7: Space lattices, 3D tilings

================

Week9: Topology: Genus, Euler-Poincare Formula, Euler Characteristic, orientrability, single-sidedness.

Punching, Zippering, Glueing Operations -- How do they affect Euler Characteristic?

Complete surface classification [Conway Ch8].

Week10: Moebius bands, cross caps, Boy's surface . . .

Week11: Turning a sphere inside out. Regular homotopies of tori and Klein bottles.

Week12: Tilings of curved spaces: Regular maps

Week13: Big Bang; the shape of the universe, the Eight-fold Way,

Symmetries in the standard model of elementary particles.

=====================================================