The structure of the set of all convex polyhedra foldable from a square is detailed. It is proved that five combinatorially distinct nondegenerate polyhedra, and four different flat polyhedra, are realizable. All the polyhedra are continuously deformable into each other, with the space of polyhedra having the topology of four connected rings.

When can a plane graph with prescribed edge lengths and prescribed angles (from among {0, 180◦, 360◦}) be folded flat to lie in an infinitesimally thick line, without crossings? This problem generalizes the classic theory of single-vertex flat origami with prescribed mountainvalley assignment, which corresponds to the case of a cycle graph. We characterize such flat-foldable plane graphs by two...

The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape ...

PURPOSE To describe a new scleral fixation foldable intraocular lens (IOL): the Ultima. METHODS The novel IOL is a new scleral fixation acrylic hydrophilic foldable lens that offers a 360 degrees sulcus support due to its round geometry. It can be folded and inserted through a 4 mm clear cornea incision. Twenty-five eyes implanted with the Ultima lens were followed for 2 years. RESULTS Twen...

Origami is the art and science of making various shapes by simply folding a sheet of paper. When origami is studied as a geometrical problem, it is often assumed that the origami is folded flat. This flat foldability is an important property when we consider applying the techniques of origami to increase the portability and storage space of industrial products. We propose a method to generate n...

Using non-rigid-foldable origami patterns to design mechanical metamaterials could potentially offer more versatile behaviors than the rigid-foldable ones, but their applications are limited by lack of analytical framework for predicting behavior. Here, we propose a theoretical model characterize square-twist pattern its rigid counterpart. Based on experimentally observed deformation mode squar...