.First and Second Rules

First, the crease pattern must be two-colorable—meaning the areas between creases can be filled with two colors so that areas of the same color never touch.Add another crease here,and the crease pattern no longer displays two-colorability.Second, the number of mountain and valley folds at any interior vertex must differ by exactly two—like the three valley folds and one mountain fold that meet here.Here’s a closer look at what happens when we make the falls at this vertex.