Singularities and Plane Maps
James J. Callahan · American Mathematical Monthly · 1974
A bit of experimenting will show that there are other possibilities; point d in Figure 1 is a new type, for instance. Further experimenting, however, leads to the conclusion that arbitrarily small alterations in the position of the fabric can eliminate any points not of the first three types. The new shape at d disappears, for example, as soon as the bottom fold is pulled to the right by any amount whatsoever (Figure 2).