(Note: This is a beta and there are bugs. Squash-folding only currently works under certain conditions.
It also seems to run slowly after a number of folds, when run as an applet.)

 

Basic Mouse Instructions:

Click left mouse button to select a corner and drag it to its new location to fold/crease/cut
Click middle mouse button and drag to create a fold-line, then click on a corner (or the general side of the line) to fold/crease/cut
Click right mouse button to select an edge and drag it to its new location to fold/crease/cut