Paper Tori

This art piece is a collaboration between myself and Fabian Lander, produced for the occasion of Rich Schwartz’ 60th Birthday Conference. It features 100 examples of embedded flat polyhedral tori with 8 vertices which were discovered with a collection of numerical search techniques. To produce the artwork, over 50,000 such tori were originally constructed, and the 100 here selected so that if you plot their moduli in Teichmüller space, the resulting 100 points trace out the outline of a 2D cartoon of a torus.