ABSTRACT
In the previous chapter, we saw how one can use circle packings to find a pattern of points within a square (or any other shape of paper) that is guaranteed to be foldable into an origami base that has a specified length and distribution of flaps. When the configuration of circles happens to match the circles (and, if needed, rivers) of known tiles, then we can fill in the crease pattern with the tile creases, and the paper can be collapsed into a base. However, a problem arises if the circle pattern matches none of the tiles we know so far. With the addition of just a few more patterns, however, we can find flatfoldable crease patterns for any circle/river packing-and for a great deal more besides.
