caa a22 4500 445804750 CHVBK 20180317145153.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00453-010-9399-8 doi (NATIONALLICENCE)springer-10.1007/s00453-010-9399-8 Origami Embedding of Piecewise-Linear Two-Manifolds [Elektronische Daten] [Marshall Bern, Barry Hayes] We show that any compact, orientable, piecewise-linear two-manifold with Euclidean metric can be realized as a flat origami, meaning a set of non-crossing polygons in Euclidean 2-space "plus layers”. This result implies a weak form of a theorem of Burago and Zalgaller: any orientable, piecewise-linear two-manifold can be embedded into Euclidean 3-space "nearly” isometrically. We also correct a mistake in our previously published construction for cutting any polygon out of a folded sheet of paper with one straight cut. Springer Science+Business Media, LLC, 2010 Disk packing nationallicence Isometric embedding nationallicence Polyhedron nationallicence Metric geometry nationallicence Bern Marshall Palo Alto Research Center, 3333 Coyote Hill Rd., 94304, Palo Alto, CA, USA aut Hayes Barry Google, Inc., 1600 Amphitheatre Parkway, 94043, Mountain View, CA, USA aut Algorithmica Springer-Verlag 59/1(2011-01-01), 3-15 0178-4617 59:1<3 2011 59 453 https://doi.org/10.1007/s00453-010-9399-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00453-010-9399-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bern Marshall Palo Alto Research Center, 3333 Coyote Hill Rd., 94304, Palo Alto, CA, USA aut NATIONALLICENCE 700 1- Hayes Barry Google, Inc., 1600 Amphitheatre Parkway, 94043, Mountain View, CA, USA aut NATIONALLICENCE 773 0- Algorithmica Springer-Verlag 59/1(2011-01-01), 3-15 0178-4617 59:1<3 2011 59 453 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer