Vicky Neale - Knitted Scarves

This rainbow of knitted scarves illustrates the seven possible types of symmetry pattern that a scarf can have ('frieze groups'), with the rule that they all have discrete translational symmetry: each is made of a repeating block. These are mathematical, infinitely long, scarves! Some have a vertical line of symmetry, some horizontal, some are symmetrical under rotation by $180^{\circ}$, and some have glide symmetry (reflection in a horizontal line followed by translation). The purple scarf has no symmetry apart from translational. The red has all the above types of symmetry. The rest have other combinations. Patterns available from https://people.maths.ox.ac.uk/neale/Frieze_groups.html. 

Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College.