Kawasaki's theorem

Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero. Crease patterns with more than one vertex do not obey such a simple criterion, and are NP-hard to fold.

The theorem is named after one of its discoverers, Toshikazu Kawasaki. However, several others also contributed to its discovery, and it is sometimes called the Kawasaki–Justin theorem or Husimi's theorem after other contributors, Jacques Justin and Kôdi Husimi.^[1]