  Miura-ori is well-known for its capability of flatly folding a sheet of paper
through a tessellated crease pattern made of repeating parallelograms. Many
potential applications have been based on the Miura-ori and its primary
variations. Here we are considering how to generalize the Miura-ori: what is
the collection of rigid-foldable creased papers with a similar quadrilateral
crease pattern as the Miura-ori? This paper reports some progress. We find some
new variations of Miura-ori with less symmetry than the known rigid-foldable
quadrilateral meshes. They are not necessarily developable or flat-foldable,
and still only have single degree of freedom in their rigid folding motion.
This article presents a classification of the new variations we discovered and
explains the methods in detail.
