  Rigid origami is examined from the perspective of rigidity theory. First and
second order rigidity are defined from local differential analysis of the
consistency constraint; while the static rigidity and prestress stability are
defined after finding the form of internal force and load. This article will
show that first-order or static rigidity implies prestress stability, which
implies second-order rigidity, which implies rigidity, but none of these is
reversible. Examples are given of rigid origami structures with these different
kinds of rigidity. Examining the different aspects of the rigidity of origami
might give a novel perspective for the development of new folding patterns, or
for the design of origami structures where some rigidity is required.
