Origami building blocks : Generic and special four-vertices
Phys. Rev. E , Volume 93 - Issue 2, Article number: 023003 p. 1- 8
Four rigid panels connected by hinges that meet at a point form a four-vertex, the fundamental building block of origami metamaterials. Most materials designed so far are based on the same four-vertex geometry, and little is known regarding how different geometries affect folding behavior. Here we systematically categorize and analyze the geometries and resulting folding motions of Euclidean four-vertices. Comparing the relative sizes of sector angles, we identify three types of generic vertices and two accompanying subtypes. We determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special four-vertices and serves as a roadmap for designing origami metamaterials.