17:
142:
42:. That is, unlike in traditional origami, the panels of the paper cannot be bent during the folding process; they must remain flat at all times, and the paper only folded along its hinges. A rigid origami model would still be foldable if it was made from glass sheets with hinges in place of its crease lines.
133:. This is true even for determining the existence of a folding motion that keeps the paper arbitrarily close to its flat state, so (unlike for other results in the hardness of folding origami crease patterns) this result does not rely on the impossibility of self-intersections of the folded paper.
173:
are commonly folded flat and then unfolded open, the standard folding pattern for doing so is not rigid; the sides of the bag bend slightly when it is folded and unfolded. The tension in the paper from this bending causes it to snap into its two flat states, the flat-folded and opened bag.
22:
21:
18:
23:
20:
84:
restrict the folding patterns that are possible, just as they do in conventional origami, but they no longer form an exact characterization: some patterns that can be folded flat in conventional origami cannot be folded flat rigidly.
19:
103:
asks whether it is possible to fold a square so the perimeter of the resulting flat figure is increased. That this can be solved within rigid origami was proved by A.S. Tarasov in 2004.
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117:
has a net with a blooming, it is not known whether there exists a blooming that does not cut across faces of the polyhedron, or whether all nets of convex polyhedra have bloomings.
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816:
374:
76:, the fold lines can be calculated rather than having to be constructed from existing lines and points. When folding rigid origami flat,
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can be folded simultaneously as a piece of rigid origami, or whether a subset of the creases can be folded, are both
873:
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908:
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that can be folded using rigid origami is restricted by its rules. Rigid origami does not have to follow the
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are toys, usually made of paper, which give an effect similar to a kaleidoscope when convoluted.
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However, there is no requirement that the structure start as a single flat sheet – for instance
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from its flat unfolded state to the folded polyhedron, or vice versa. Although every
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370:"Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings"
552:
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559:
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691:
526:
388:
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for a Miura fold. The parallelograms of this example have 84° and 96° angles.
38:
which is concerned with folding structures using flat rigid sheets joined by
851:
141:
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365:
273:
186:
160:
arrays for space satellites, which have to be folded before deployment.
166:
has applied rigid origami to the problem of folding a space telescope.
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35:
498:
Abstracts from the 14th Annual Fall
Workshop on Computational Geometry
224:
716:
452:
140:
39:
15:
563:
258:(2016). "Rigid origami vertices: conditions and forcing sets".
56:, and rigid origami structures can be considered as a type of
49:
with flat bottoms are studied as part of rigid origami.
27:
One-DOF Superimposed Rigid
Origami with Multiple States
189:
which are a form of rigid origami and the flexatube.
861:
808:
787:
730:
684:
653:
597:
156:is a rigid fold that has been used to pack large
219:(PhD thesis). University of Waterloo, Canada.
575:
339:"Solution of Arnold's "folded ruble" problem"
60:. Rigid origami has great practical utility.
8:
510:: CS1 maint: multiple names: authors list (
52:Rigid origami is a part of the study of the
582:
568:
560:
451:
387:
96:has constant volume when flexed rigidly.
204:
503:
375:Discrete & Computational Geometry
125:Determining whether all creases of a
7:
817:Geometric Exercises in Paper Folding
838:A History of Folding in Mathematics
500:. Cambridge, Massachusetts: 14–15.
312:Beiträge zur Algebra und Geometrie
238:Abel, Zachary; Cantarella, Jason;
14:
439:Journal of Computational Geometry
261:Journal of Computational Geometry
306:; Sabitov, I.; Walz, A. (1997).
738:Alexandrov's uniqueness theorem
109:is a rigid origami motion of a
468:"The Eyeglass Space Telescope"
434:"Rigid foldability is NP-hard"
1:
676:Regular paperfolding sequence
494:"Folding Paper Shopping Bags"
824:Geometric Folding Algorithms
591:Mathematics of paper folding
349:(1): 174–187. Archived from
54:mathematics of paper folding
1001:
874:Margherita Piazzola Beloch
645:Yoshizawa–Randlett system
389:10.1007/s00454-008-9052-3
845:Origami Polyhedra Design
308:"The bellows conjecture"
68:The number of standard
337:Tarasov, A. S. (2004).
635:Napkin folding problem
149:
101:napkin folding problem
28:
980:Linkages (mechanical)
424:; Horiyama, Takashi;
343:Chebyshevskii Sbornik
217:Folding and Unfolding
144:
26:
795:Fold-and-cut theorem
751:Steffen's polyhedron
615:Huzita–Hatori axioms
605:Big-little-big lemma
410:. Announced in 2003.
274:10.20382/jocg.v7i1a9
74:Huzita–Hatori axioms
743:Flexible polyhedron
525:Weisstein, Eric W.
484:Devin. J. Balkcom,
111:net of a polyhedron
94:flexible polyhedron
924:Toshikazu Kawasaki
747:Bricard octahedron
722:Yoshimura buckling
620:Kawasaki's theorem
150:
78:Kawasaki's theorem
58:mechanical linkage
29:
967:
966:
831:Geometric Origami
702:Paper bag problem
625:Maekawa's theorem
531:Wolfram MathWorld
492:(November 2004).
490:Martin L. Demaine
178:Recreational uses
121:Complexity theory
115:convex polyhedron
82:Maekawa's theorem
24:
992:
904:David A. Huffman
869:Roger C. Alperin
772:Source unfolding
640:Pureland origami
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382:(1–3): 339–388.
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250:; Ku, Jason S.;
240:Demaine, Erik D.
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185:has popularised
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949:Joseph O'Rourke
884:Robert Connelly
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712:Schwarz lantern
697:Modular origami
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553:"Rigid Origami"
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486:Erik D. Demaine
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430:Tachi, Tomohiro
420:Akitaya, Hugo;
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256:Tachi, Tomohiro
252:Lang, Robert J.
248:Hull, Thomas C.
244:Eppstein, David
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169:Although paper
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90:Bellows theorem
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34:is a branch of
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954:Tomohiro Tachi
951:
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929:Robert J. Lang
926:
921:
919:Humiaki Huzita
916:
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899:Rona Gurkewitz
896:
894:Martin Demaine
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777:Star unfolding
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610:Crease pattern
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542:External links
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364:Miller, Ezra;
356:
353:on 2007-08-25.
345:(in Russian).
329:
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268:(1): 171–184.
230:
213:Demaine, E. D.
203:
202:
200:
197:
183:Martin Gardner
179:
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164:Robert J. Lang
146:Crease pattern
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127:crease pattern
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800:Lill's method
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788:Miscellaneous
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707:Rigid origami
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685:3d structures
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654:Strip folding
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428:; Ku, Jason;
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422:Demaine, Erik
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193:Kaleidocycles
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171:shopping bags
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70:origami bases
63:
61:
59:
55:
50:
48:
47:shopping bags
43:
41:
37:
33:
32:Rigid origami
959:Eve Torrence
889:Erik Demaine
850:
843:
836:
829:
822:
815:
809:Publications
706:
671:Möbius strip
661:Dragon curve
598:Flat folding
530:
520:
506:cite journal
497:
479:
462:
443:
437:
426:Hull, Thomas
415:
379:
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351:the original
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304:Connelly, R.
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168:
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151:
137:Applications
124:
105:
98:
92:says that a
87:
67:
51:
44:
31:
30:
944:KĹŤryĹŤ Miura
939:Jun Maekawa
914:KĂ´di Husimi
630:Map folding
527:"Flexatube"
318:(1): 1–10.
158:solar panel
64:Mathematics
974:Categories
934:Anna Lubiw
767:Common net
692:Miura fold
453:1812.01160
225:10012/1068
199:References
154:Miura fold
852:Origamics
731:Polyhedra
549:Hull, Tom
366:Pak, Igor
187:flexagons
909:Tom Hull
879:Yan Chen
762:Blooming
666:Flexagon
432:(2020).
406:10227925
368:(2008).
215:(2001).
107:Blooming
985:Origami
398:2383765
324:1447981
290:7181079
282:3491092
131:NP-hard
36:origami
862:People
717:Sonobe
404:
396:
322:
288:
280:
40:hinges
471:(PDF)
448:arXiv
446:(1).
402:S2CID
286:S2CID
512:link
152:The
99:The
88:The
80:and
757:Net
384:doi
270:doi
221:hdl
976::
749:,
551:.
529:.
508:}}
504:{{
496:.
488:,
444:11
442:.
436:.
400:.
394:MR
392:.
380:39
378:.
372:.
341:.
320:MR
316:38
314:.
310:.
284:.
278:MR
276:.
264:.
254:;
246:;
242:;
753:)
745:(
583:e
576:t
569:v
555:.
533:.
514:)
473:.
456:.
450::
408:.
386::
347:5
326:.
292:.
272::
266:7
227:.
223::
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