相关论文: Origami constructions

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit…

We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…

Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe…

Flat-foldability problem of origami is the problem to determine whether a given crease pattern drawn on a piece of paper is possible to fold without any penetration or intrusion of a polygon into any connections among them. It is known from…

This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results…

Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve…

Origami, which transforms flat sheets into three-dimensional shapes through folding patterns, has inspired the emergence of deployable systems in architecture and civil realms. Most existing origami-inspired deployable systems are based on…

In the context of interactive proofs, a "folding scheme" (popularized by Nova) is a way to combine multiple instances of a constraint system into a single instance, so the validity of the multiple instances can statistically be reduced to…

Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found…

The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.

We characterize the phase-space of all Helical Miura Origami. These structures are obtained by taking a partially folded Miura parallelogram as the unit cell, applying a generic helical or rod group to the cell, and characterizing all the…

A new construction of the real number system, that is built directly upon the additive group of integers and has its roots in the definition due to Henri Poincar\'e of the rotation number of an orientation preserving homeomorphism of the…

We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredients. The first is a framework that allows us to think of such…

Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their…

Creating complex spatial objects from a flat sheet of material using origami folding techniques has attracted attention in science and engineering. In the present work, we employ geometric properties of partially folded zigzag strips to…

We introduce a simple and concrete way of visualizing in three dimensions a "flat" Klein bottle -- one whose local intrinsic geometry is the same as that of a flat plane -- which preserves most its topological and geometric structure.…

Foldable paper constructions known as flexagons have been studied since 1939. In this paper we review the construction of hexagonal flexagons (hexaflexagons) and compute the number of distinct hexaflexagons with n faces.

Programmable folding of elastic sheets typically relies on predefined flexible creases or active materials-enabled hinges, which lack intrinsic bistability and limit reprogrammability within a single structure. Here, we present a…

We present a method of construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for $U=0$ and $U\rightarrow\infty$. These states are localized in what concerns both hole and particle movement.…