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on its surface, cutting the polyhedron on the cut locus will produce a result that can be unfolded into a flat plane, producing the source unfolding. The resulting net may, however, cut across some of the faces of the polyhedron rather than only cutting along its edges.
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The source unfolding can also be continuously transformed from the polyhedron to its flat net, keeping flat the parts of the net that do not lie along edges of the polyhedron, as a
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278:(2008), "Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings",
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143:, cutting the surface of the polytope into a net that can be unfolded into a flat
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264:. Announced at the Japan Conference on Computational Geometry and Graphs, 2009.
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of the polyhedron. The unfolded shape of the source unfolding is always a
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An analogous unfolding method can be applied to any higher-dimensional
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of a point on the surface of the polyhedron. The cut locus of a point
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consists of all points on the surface that have two or more shortest
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80:. For every convex polyhedron, and every choice of the point
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219:(2011), "Continuous blooming of convex polyhedra",
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180:, Cambridge University Press, pp. 359–362,
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32:obtained by cutting the polyhedron along the
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281:Discrete & Computational Geometry
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571:Geometric Exercises in Paper Folding
592:A History of Folding in Mathematics
174:(2007), "24.1.1 Source unfolding",
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492:Alexandrov's uniqueness theorem
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430:Regular paperfolding sequence
132:; this is in contrast to the
578:Geometric Folding Algorithms
345:Mathematics of paper folding
177:Geometric Folding Algorithms
760:
628:Margherita Piazzola Beloch
399:Yoshizawa–Randlett system
295:10.1007/s00454-008-9052-3
245:10.1007/s00373-011-1024-3
599:Origami Polyhedra Design
222:Graphs and Combinatorics
744:Computational geometry
389:Napkin folding problem
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50:
18:computational geometry
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549:Fold-and-cut theorem
505:Steffen's polyhedron
369:Huzita–Hatori axioms
359:Big-little-big lemma
307:. Announced in 2003.
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40:
497:Flexible polyhedron
110:star-shaped polygon
678:Toshikazu Kawasaki
501:Bricard octahedron
476:Yoshimura buckling
374:Kawasaki's theorem
205:Demaine, Martin L.
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585:Geometric Origami
456:Paper bag problem
379:Maekawa's theorem
213:Langerman, Stefan
187:978-0-521-71522-5
125:{\displaystyle p}
93:{\displaystyle p}
73:{\displaystyle p}
49:{\displaystyle p}
26:convex polyhedron
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658:David A. Huffman
623:Roger C. Alperin
526:Source unfolding
394:Pureland origami
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288:(1–3): 339–388,
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217:O'Rourke, Joseph
211:; Iacono, John;
201:Demaine, Erik D.
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22:source unfolding
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466:Schwarz lantern
451:Modular origami
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236:10.1.1.150.9715
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141:convex polytope
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531:Star unfolding
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274:Miller, Ezra;
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229:(3): 363–376,
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542:Miscellaneous
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713:Eve Torrence
643:Erik Demaine
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563:Publications
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425:Möbius strip
415:Dragon curve
352:Flat folding
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698:KĹŤryĹŤ Miura
693:Jun Maekawa
668:KĂ´di Husimi
384:Map folding
728:Categories
688:Anna Lubiw
521:Common net
446:Miura fold
151:References
145:hyperplane
739:Polyhedra
606:Origamics
485:Polyhedra
276:Pak, Igor
231:CiteSeerX
58:geodesics
34:cut locus
734:Polygons
663:Tom Hull
633:Yan Chen
516:Blooming
420:Flexagon
209:Hart, Vi
106:blooming
304:2383765
253:2787423
616:People
471:Sonobe
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184:
20:, the
261:82408
257:S2CID
28:is a
24:of a
182:ISBN
511:Net
290:doi
241:doi
60:to
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16:In
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300:MR
298:,
286:39
284:,
255:,
249:MR
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227:27
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215:;
207:;
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170:;
159:^
147:.
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499:(
337:e
330:t
323:v
292::
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120:p
88:p
68:p
44:p
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