ABSTRACT
For flat origami tessellations, one of the key constraints in their design is the Kawasaki-Justin condition (KJC), a condition found and described independently by Toshikazu Kawasaki [Takahama and Kasahara 85] and Jacques Justin [Justin 86]. There are several equivalent formulations, but the most common is the following: A crease pattern can be folded flat only if, at every interior vertex,
α1 − α2 + α3 − α4 . . . = 0, (1)
where the {αi} are the sector angles around the vertex, numbered cyclically. The Kawasaki-Justin condition is not sufficient for flat-foldability;
additional conditions apply to the crease assignment and layer ordering (also formulated by Justin, see [Justin 97]). However, in many situations, the primary challenge in designing an origami crease pattern is assuring that it satisfies KJC.
