Fig. 2.

Folding of helicoids ($K<0$). Composite image of Movie S1 demonstrates the folding behavior of a creased helicoid with a clamped edge, indented with a rigid indenter. Schematics for all cases indicate the position of the crease relative to the asymptotic curves with ${\kappa }_N=0$ (dotted black or yellow). (A) Five frames at equal time interval depict the discontinuous snap-through deformation of a helicoid possessing a crease with ${\kappa }_N\ne 0$ from initial folded state (0) to the final folded state (+4). Frame 3 falls midsnap, and is blurred. For both (B) planar (along generating line) and (C) nonplanar (or helical) ${\kappa }_N=0$ creases, a composite image is used to depict torsion along either side of the folded state (0) of the crease. As predicted, a continuous deformation characteristic of a hinge is observed for both of these cases. Frames at equal time intervals on either side are used (1, 2 on one side, and i, ii on another).