  Minimizing the elastic free energy of a thin sheet of nematic polymer network
among smooth isometric immersions is the strategy purported by the mainstream
theory. In this paper, we broaden the class of admissible spontaneous
deformations: we consider ridged isometric immersions, which can cause a sharp
ridge in the immersed surfaces. We propose a model to compute the extra energy
distributed along such ridges. This energy comes from bending; it is shown
under what circumstances it scales quadratically with the sheet's thickness,
falling just in between stretching and bending energies. We put our theory to
the test by studying the spontaneous deformation of a disk on which a radial
hedgehog was imprinted at the time of crosslinking. We predict the number of
folds that develop in terms of the degree of order induced in the material by
external agents (such as heat and illumination).
