In this paper, a method is proposed for geometrically constructing thick panel structures that follow the kinetic behavior of rigid origami by using tapered or two-ply panels and hinges located at their edges. The proposed method can convert generalized pattern of rigid-foldable origami into thick panels structure with kinetic motion, which leads to novel designs of origami for various engineer...

Scaffolded DNA origami has proven to be a versatile method for generating functional nanostructures with prescribed sub-100 nm shapes. Programming DNA-origami tiles to form large-scale 2D lattices that span hundreds of nanometers to the micrometer scale could provide an enabling platform for diverse applications ranging from metamaterials to surface-based biophysical assays. Toward this end, he...

DNA origami provides a versatile platform for conducting 'architecture-function' analysis to determine how the nanoscale organization of multiple copies of a protein component within a multi-protein machine affects its overall function. Such analysis requires that the copy number of protein molecules bound to the origami scaffold exactly matches the desired number, and that it is uniform over a...

Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there have been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid ...

Origami is the art of folding pieces of paper into works of sculpture without the aid of scissors or glue. Modern advancements in the complexity of origami (e.g., the work of Montroll and Maekawa) reveal a rich geometric structure governing the possibilities of paperfolding. In this paper we initiate a mathematical study of this \origami geometry" and explore the possibilities of a graph the-or...

This work studies the structure of origami bases via graph drawings of origami polyhedra. In particular, we propose a new class of polyhedra, called extreme-base polyhedra, that capture the essence of \extreme" origami bases. We develop a linear-time algorithm to nd the \natural" straight-line planar drawing of these polyhedra. This algorithm demonstrates a recursive structure in the polyhedra ...

Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which ...

In origami geometry, the construction and the verification should go hand in hand. When we present a new origami by a new fold method, we will show certain geometric properties that enable us to claim its novelty by formal argument, i.e. proving. It is desirable to have some kind of automation by a computer towards computer-aided origami. Several systems have been implemented to simulate and tr...

The purest form of origami is widely considered to be: folding only, from an uncut square. This purity is, of course, a modern innovation, as historical origami included both cuts and odd-sized sheets of paper, and the 20th-century blossoming of origami in Japan and the west used multiple sheets for both composite and modular folding. That diversity of starting material continues today. Composi...

Two results in “computational origami” are illustrated. Computational geometry has recently been applied to solve two open problems in “origami mathematics.”