Details

The folding angle represents the angle by which one specific crease is folded, which then determines the folding angles of all the other creases (folding angle = - the dihedral angle of the crease). The crease angle is the acute angle of the parallelogram which is tiled to make the crease pattern. The value crease angle = is a singularity of the folding equations; the creases cannot all collapse simultaneously when the parallelograms are perfect squares (they would have to be folded sequentially, like a regular road map). For some history of the Miura map fold, more information is online.