{"oa_version":"Preprint","publisher":"American Physiological Society","oa":1,"abstract":[{"lang":"eng","text":"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."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"03","volume":93,"date_updated":"2021-01-12T06:49:10Z","intvolume":"        93","article_number":"023003","date_published":"2016-02-03T00:00:00Z","quality_controlled":"1","publication":"Physical Review E - Statistical, Nonlinear, and Soft Matter Physics","doi":"10.1103/PhysRevE.93.023003","month":"02","external_id":{"arxiv":["1507.08442"]},"year":"2016","type":"journal_article","title":"Origami building blocks: Generic and special four-vertices","citation":{"ista":"Waitukaitis SR, Van Hecke M. 2016. Origami building blocks: Generic and special four-vertices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 93(2), 023003.","mla":"Waitukaitis, Scott R., and Martin Van Hecke. “Origami Building Blocks: Generic and Special Four-Vertices.” <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>, vol. 93, no. 2, 023003, American Physiological Society, 2016, doi:<a href=\"https://doi.org/10.1103/PhysRevE.93.023003\">10.1103/PhysRevE.93.023003</a>.","chicago":"Waitukaitis, Scott R, and Martin Van Hecke. “Origami Building Blocks: Generic and Special Four-Vertices.” <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>. American Physiological Society, 2016. <a href=\"https://doi.org/10.1103/PhysRevE.93.023003\">https://doi.org/10.1103/PhysRevE.93.023003</a>.","apa":"Waitukaitis, S. R., &#38; Van Hecke, M. (2016). Origami building blocks: Generic and special four-vertices. <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>. American Physiological Society. <a href=\"https://doi.org/10.1103/PhysRevE.93.023003\">https://doi.org/10.1103/PhysRevE.93.023003</a>","ama":"Waitukaitis SR, Van Hecke M. Origami building blocks: Generic and special four-vertices. <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>. 2016;93(2). doi:<a href=\"https://doi.org/10.1103/PhysRevE.93.023003\">10.1103/PhysRevE.93.023003</a>","short":"S.R. Waitukaitis, M. Van Hecke, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 93 (2016).","ieee":"S. R. Waitukaitis and M. Van Hecke, “Origami building blocks: Generic and special four-vertices,” <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>, vol. 93, no. 2. American Physiological Society, 2016."},"status":"public","date_created":"2018-12-11T11:44:44Z","publist_id":"7932","_id":"122","extern":"1","acknowledgement":"This work is part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO).","issue":"2","language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.08442"}],"author":[{"id":"3A1FFC16-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2299-3176","full_name":"Waitukaitis, Scott R","last_name":"Waitukaitis","first_name":"Scott R"},{"first_name":"Martin","last_name":"Van Hecke","full_name":"Van Hecke, Martin"}]}