  In this paper, we will show methods to interpret some rigid origami with
higher degree vertices as the limit case of structures with degree-4
supplementary angle vertices. The interpretation is based on separating each
crease into two parallel creases, or \emph{double lines}, connected by
additional structures at the vertex. We show that double-lined versions of
degree-4 flat-foldable vertices possess a rigid folding motion, as do symmetric
degree-$2n$ vertices. The latter gives us a symbolic analysis of the original
vertex, showing that the tangent of the quarter fold angles are proportional to
each other. The double line method is also a potentially useful in giving
thickness to rigid origami mechanisms. By making single crease into two
creases, the fold angles can be distributed to avoid $180^\circ$ folds, when
panels can easily collide with each other. This can be understood as an
extension of the crease offset method of thick rigid origami with an additional
guarantee of rigid-foldability.
