Helix, Ring, and Bracelet

There are four types of closed paths one can form on a torus:
  1. R-Helix - Right handed helix
  2. L-Helix - Left handed helix
  3. Ring - Non-helical path surrounding circular axis
  4. Bracelet - Non-helical path surrounding linear axis

Winning conditions for Black: Form a ring, an r-helix, or any
combination of two or more closed path types.

Winning conditions for White: Form a bracelet, an l-helix, or any
combination of two or more closed path types.