Abstract

A quadrilateral creased paper is the union of a 2-manifold and a quadrilateral mesh embedded on this 2-manifold, which is not necessarily developable. The ``Rigid-foldability’’ we discuss here corresponds to flexibility in rigidity theory, where each quadrilateral is considered as a rigid panel. Based on a nearly-complete classification of rigid-foldable Kokotsakis quadrilaterals from Ivan Izmestiev, here we will show new discoveries on the large rigid-foldable quadrilateral creased papers with the following additional requirements: 1) For at least one rigid folding motion no folding angle remains constant. 2) The quadrilateral creased paper can be extended in both longitudinal and transverse directions infinitely. 3) The sector angles can be solved quadrilateral by quadrilateral. All these quadrilateral creased papers have one degree of freedom in each branch of their rigid folding motion. We also explore how these new variations of large rigid-foldable quadrilateral creased papers can be used to approximate a non-developable surface. The approximation is started from the planar state, then the creased paper can be folded continuously to the final state, where the folding motion halts because some panels clash.