117:
105:
79:
22:
313:
97:
125:
160:
192:
150:
technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. These insertions create tension or
175:
The additional restrictions that distinguish modular origami from other forms of multi-piece origami are using many identical copies of any folded unit, and linking them together in a symmetrical or repeating fashion to complete the model. There is a common misconception that treats all multi-piece
171:
Modular origami can be classified as a sub-set of multi-piece origami, since the rule of restriction to one sheet of paper is abandoned. However, all the other rules of origami still apply, so the use of glue, thread, or any other fastening that is not a part of the sheet of paper is not generally
427:
Each module joins others at the vertices of a polyhedron to form a polygonal face. The tabs form angles on opposite sides of an edge. For example, a subassembly of three triangle corners forms a triangle, the most stable configuration. As the internal angle increases for squares, pentagons and so
261:
in Japan. The 1970s saw a sudden period of interest and development in modular origami as its own distinct field, leading to its present status in origami folding. One notable figure is Steve
Krimball, who discovered the potential in
455:
The
Mukhopadhyay module can form any equilateral polyhedron. Each unit has a middle crease that forms an edge, and triangular wings that form adjacent stellated faces. For example, a cuboctahedral assembly has 24 units, since the
391:
angles. Each module has two pockets and two tabs, on opposite sides. The angle of each tab can be changed independently of the other tab. Each pocket can receive tabs of any angle. The most common angles form polygonal faces:
435:
has one square face and four triangular faces. This requires hybrid modules, or modules having different angles. A pyramid consists of eight modules, four modules as square-triangle, and four as triangle-triangle.
209:. It contains a print that shows a group of traditional origami models, one of which is a modular cube. The cube is pictured twice (from slightly different angles) and is identified in the accompanying text as a
222:(published in 1965) appears to have the same model, where it is called a "cubical box". The six modules required for this design were developed from the traditional Japanese paperfold commonly known as the
362:. Macro-modular origami is a form of modular origami in which finished assemblies are themselves used as the building blocks to create larger integrated structures. Such structures are described in
253:
Most traditional designs are however single-piece and the possibilities inherent in the modular origami idea were not explored further until the 1960s when the technique was re-invented by
183:
of module can still be used. Typically this means using separate linking units hidden from sight to hold parts of the construction together. Any other usage is generally discouraged.
866:
269:
Since then, the modular origami technique has been popularized and developed extensively, and now there have been thousands of designs developed in this repertoire.
116:
859:
439:
Further polygonal faces are possible by altering the angle at each corner. The Neale modules can form any equilateral polyhedron including those having
468:
and other stellated polyhedra. The
Mukhopadhyay module works best when glued together, especially for polyhedra having larger numbers of sides.
852:
687:
662:
582:
546:
1101:
43:
1122:
598:
331:
Modular origami techniques can be used to create a wide range of lidded boxes in many shapes. Many examples of such boxes are shown in
1022:
732:
703:
629:
65:
205:
The first historical evidence for a modular origami design comes from a
Japanese book by Hayato Ohoka published in 1734 called
1163:
754:
1233:
929:
464:
are possible, by folding the central crease on each module outwards or convexly instead of inwards or concavely as for the
151:
friction that holds the model together. Some assemblies can be somewhat unstable because adhesives or string are not used.
960:
784:
1108:
875:
239:
is sometimes, rather inaccurately, used to describe any three-dimensional modular origami structure resembling a ball.
36:
30:
104:
1158:
273:
254:
899:
47:
1193:
1129:
285:
229:
There are several other traditional
Japanese modular designs, including balls of folded paper flowers known as
235:, or medicine balls. These designs are not integrated and are commonly strung together with thread. The term
1035:
919:
819:
266:
and demonstrated that it could be used to make alternative polyhedral shapes, including a 30-piece ball.
798:
904:
78:
1079:
909:
889:
511:
444:
243:
211:
1264:
1046:
1027:
840:
Kusudama by
Mikhail Puzakov & Ludmila Puzakova: models, folding instruction, history, geometry
1208:
1031:
1006:
697:
432:
839:
359:
1228:
1115:
986:
750:
728:
683:
658:
635:
625:
578:
552:
542:
484:
405:
388:
281:
1269:
1188:
1153:
1084:
1056:
1041:
924:
606:
324:(sometimes known as coasters), stars, rotors, and rings. Three-dimensional forms tend to be
312:
258:
96:
776:
120:
The page from Ranma zushiki 欄間図式 Volume 3 (1734) where modular origami models are depicted.
1168:
996:
788:
955:
1238:
1213:
1203:
1198:
1183:
1178:
1061:
894:
293:
1258:
991:
457:
124:
1243:
1173:
945:
808:
289:
814:
1223:
914:
742:
720:
465:
384:
363:
332:
277:
132:
109:
84:
844:
781:
320:
Modular origami forms may be flat or three-dimensional. Flat forms are usually
1218:
1051:
976:
461:
325:
247:
159:
556:
89:
1136:
639:
129:
824:
536:
830:
Kusudama Me! Kusudamas of
Lukasheva Ekaterina, also diagrams and tutorials
246:
tradition, notably the pagoda (from Maying Soong) and the lotus made from
191:
950:
412:
398:
355:
231:
197:
794:
Photo
Gallery and Folding Instructions For Many Polyhedra and Variations
440:
419:
321:
147:
1001:
682:(First ed.). Tokyo ; Rutland, Vermont: Tuttle Publishing.
263:
164:
297:
431:
Many polyhedra call for unalike adjacent polygons. For example, a
311:
190:
158:
123:
115:
103:
95:
77:
803:
538:
Ornamental origami: exploring 3D geomentric [sic] designs
848:
163:
Examples of modular origami made up of different variations of
770:
108:
Modular origami hexagonal box with six-petal lid. Designed by
15:
834:
793:
354:
There are some modular origami that are approximations of
829:
301:
201:, the traditional Japanese precursor to modular origami
773:
Learn how to 3d
Origami, tutorials and artist network.
815:
Mukhopadhyay's super simple isosceles triangle module
226:. Each module forms one face of the finished cube.
88:
designed by
Bennett Arnstein. Diagrammed in the book
1146:
1093:
1072:
1015:
969:
938:
882:
778:3D origami video tutorials by Arthur Vershigora.
835:Paper Structures by Krystyna and Wojtek Burczyk
725:Unit Origami: Multidimensional Transformations
599:"David Lister on Origins of the Sonobe Module"
577:(14. Pr ed.). Tokyo: Japan Publications.
575:Unit origami: multidimensional transformations
90:3-D Geometric Origami: Modular Polyhedra (1995
860:
368:Unit Origami-Multidimensional Transformations
8:
820:James S. Plank's Penultimate Modular Origami
242:There are also a few modular designs in the
867:
853:
845:
512:"illustrated book; print | British Museum"
66:Learn how and when to remove this message
657:. TĹŤkyĹŤ: Japan Publications Trading Co.
272:Notable modular origami artists include
29:This article includes a list of general
476:
695:
328:or tessellations of simple polyhedra.
485:"Golden Venture Folding | 3D Origami"
100:An example of golden venture folding.
7:
1102:Geometric Exercises in Paper Folding
624:. Tokyo, Japan: Japan Publications.
568:
566:
506:
504:
1123:A History of Folding in Mathematics
799:Image of Menger's Sponge in origami
383:Neale developed a system to model
378:
35:it lacks sufficient corresponding
14:
811:Paper model of a Geodesic Sphere.
379:Robert Neale's penultimate module
428:forth, the stability decreases.
387:based on a module with variable
20:
1023:Alexandrov's uniqueness theorem
172:acceptable in modular origami.
825:Oxi Module by Michał Kosmulski
749:. Japan Publications Trading.
541:. Wellesley, Mass: AK Peters.
1:
961:Regular paperfolding sequence
702:: CS1 maint: date and year (
1109:Geometric Folding Algorithms
876:Mathematics of paper folding
460:has 24 edges. Additionally,
680:Tomoko Fuse's origami boxes
535:Mukerji, Meenakshi (2009).
349:Tomoko Fuse's Origami Boxes
155:Definition and restrictions
1286:
1159:Margherita Piazzola Beloch
316:Modules of modular origami
215:(magic treasure chest).
930:Yoshizawa–Randlett system
1130:Origami Polyhedra Design
603:www.britishorigami.info
489:Origami Resource Center
257:in the US and later by
135:made from custom papers
50:more precise citations.
920:Napkin folding problem
747:Fabulous Origami Boxes
727:. Japan Publications.
655:Fabulous origami boxes
341:Fabulous Origami Boxes
317:
202:
168:
136:
121:
113:
101:
93:
678:Fuse, Tomoko (2018).
653:Fuse, Tomoko (1998).
620:Fuse, Tomoko (1989).
573:Fusè, Tomoko (2009).
516:www.britishmuseum.org
385:equilateral polyhedra
315:
194:
162:
127:
119:
107:
99:
81:
1080:Fold-and-cut theorem
1036:Steffen's polyhedron
900:Huzita–Hatori axioms
890:Big-little-big lemma
804:Modular origami page
472:Notes and references
445:rhombic dodecahedron
276:, Mitsunobu Sonobe,
244:Chinese paperfolding
176:origami as modular.
1028:Flexible polyhedron
451:Mukhopadhyay module
302:Ekaterina Lukasheva
1209:Toshikazu Kawasaki
1032:Bricard octahedron
1007:Yoshimura buckling
905:Kawasaki's theorem
787:2012-06-09 at the
318:
264:Sonobe's cube unit
203:
169:
137:
122:
114:
102:
94:
1252:
1251:
1116:Geometric Origami
987:Paper bag problem
910:Maekawa's theorem
809:Origami Geosphere
782:Kusudama Pictures
689:978-0-8048-5006-3
664:978-0-87040-978-3
584:978-0-87040-852-6
548:978-1-56881-445-2
326:regular polyhedra
298:Meenakshi Mukerji
282:Kunihiko Kasahara
146:is a multi-stage
76:
75:
68:
1277:
1189:David A. Huffman
1154:Roger C. Alperin
1057:Source unfolding
925:Pureland origami
869:
862:
855:
846:
771:3dOrigamiArt.com
760:
738:
708:
707:
701:
693:
675:
669:
668:
650:
644:
643:
617:
611:
610:
605:. Archived from
595:
589:
588:
570:
561:
560:
532:
526:
525:
523:
522:
508:
499:
498:
496:
495:
481:
443:faces, like the
374:Modeling systems
259:Mitsunobu Sonobe
220:World of Origami
71:
64:
60:
57:
51:
46:this article by
37:inline citations
24:
23:
16:
1285:
1284:
1280:
1279:
1278:
1276:
1275:
1274:
1255:
1254:
1253:
1248:
1234:Joseph O'Rourke
1169:Robert Connelly
1142:
1089:
1068:
1011:
997:Schwarz lantern
982:Modular origami
965:
934:
878:
873:
789:Wayback Machine
767:
757:
741:
735:
719:
716:
711:
694:
690:
677:
676:
672:
665:
652:
651:
647:
632:
619:
618:
614:
597:
596:
592:
585:
572:
571:
564:
549:
534:
533:
529:
520:
518:
510:
509:
502:
493:
491:
483:
482:
478:
474:
453:
425:
381:
376:
360:Menger's sponge
310:
189:
157:
140:Modular origami
72:
61:
55:
52:
42:Please help to
41:
25:
21:
12:
11:
5:
1283:
1281:
1273:
1272:
1267:
1257:
1256:
1250:
1249:
1247:
1246:
1241:
1239:Tomohiro Tachi
1236:
1231:
1226:
1221:
1216:
1214:Robert J. Lang
1211:
1206:
1204:Humiaki Huzita
1201:
1196:
1191:
1186:
1184:Rona Gurkewitz
1181:
1179:Martin Demaine
1176:
1171:
1166:
1161:
1156:
1150:
1148:
1144:
1143:
1141:
1140:
1133:
1126:
1119:
1112:
1105:
1097:
1095:
1091:
1090:
1088:
1087:
1082:
1076:
1074:
1070:
1069:
1067:
1066:
1065:
1064:
1062:Star unfolding
1059:
1054:
1049:
1039:
1025:
1019:
1017:
1013:
1012:
1010:
1009:
1004:
999:
994:
989:
984:
979:
973:
971:
967:
966:
964:
963:
958:
953:
948:
942:
940:
936:
935:
933:
932:
927:
922:
917:
912:
907:
902:
897:
895:Crease pattern
892:
886:
884:
880:
879:
874:
872:
871:
864:
857:
849:
843:
842:
837:
832:
827:
822:
817:
812:
806:
801:
796:
791:
779:
774:
766:
765:External links
763:
762:
761:
755:
739:
733:
715:
712:
710:
709:
688:
670:
663:
645:
630:
612:
609:on 2009-06-05.
590:
583:
562:
547:
527:
500:
475:
473:
470:
452:
449:
424:
423:
416:
409:
402:
394:
380:
377:
375:
372:
309:
306:
294:Rona Gurkewitz
188:
185:
179:More than one
156:
153:
83:Triangle Edge
74:
73:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
1282:
1271:
1268:
1266:
1263:
1262:
1260:
1245:
1242:
1240:
1237:
1235:
1232:
1230:
1227:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1182:
1180:
1177:
1175:
1172:
1170:
1167:
1165:
1162:
1160:
1157:
1155:
1152:
1151:
1149:
1145:
1139:
1138:
1134:
1132:
1131:
1127:
1125:
1124:
1120:
1118:
1117:
1113:
1111:
1110:
1106:
1104:
1103:
1099:
1098:
1096:
1092:
1086:
1085:Lill's method
1083:
1081:
1078:
1077:
1075:
1073:Miscellaneous
1071:
1063:
1060:
1058:
1055:
1053:
1050:
1048:
1045:
1044:
1043:
1040:
1037:
1033:
1029:
1026:
1024:
1021:
1020:
1018:
1014:
1008:
1005:
1003:
1000:
998:
995:
993:
992:Rigid origami
990:
988:
985:
983:
980:
978:
975:
974:
972:
970:3d structures
968:
962:
959:
957:
954:
952:
949:
947:
944:
943:
941:
939:Strip folding
937:
931:
928:
926:
923:
921:
918:
916:
913:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
887:
885:
881:
877:
870:
865:
863:
858:
856:
851:
850:
847:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
810:
807:
805:
802:
800:
797:
795:
792:
790:
786:
783:
780:
777:
775:
772:
769:
768:
764:
758:
752:
748:
744:
740:
736:
734:0-87040-852-6
730:
726:
722:
718:
717:
713:
705:
699:
691:
685:
681:
674:
671:
666:
660:
656:
649:
646:
641:
637:
633:
631:0-87040-821-6
627:
623:
622:Origami Boxes
616:
613:
608:
604:
600:
594:
591:
586:
580:
576:
569:
567:
563:
558:
554:
550:
544:
540:
539:
531:
528:
517:
513:
507:
505:
501:
490:
486:
480:
477:
471:
469:
467:
463:
459:
458:cuboctahedron
450:
448:
446:
442:
437:
434:
429:
421:
418:120 degrees (
417:
414:
411:108 degrees (
410:
407:
403:
400:
396:
395:
393:
390:
386:
373:
371:
369:
366:'s 1990 book
365:
361:
357:
352:
350:
346:
342:
338:
337:Origami Boxes
334:
329:
327:
323:
314:
307:
305:
303:
299:
295:
291:
287:
283:
279:
275:
270:
267:
265:
260:
256:
251:
249:
245:
240:
238:
234:
233:
227:
225:
221:
218:Isao Honda's
216:
214:
213:
208:
207:Ranma Zushiki
200:
199:
193:
186:
184:
182:
177:
173:
166:
161:
154:
152:
149:
148:paper folding
145:
141:
134:
131:
126:
118:
111:
106:
98:
91:
87:
86:
80:
70:
67:
59:
49:
45:
39:
38:
32:
27:
18:
17:
1244:Eve Torrence
1174:Erik Demaine
1135:
1128:
1121:
1114:
1107:
1100:
1094:Publications
981:
956:Möbius strip
946:Dragon curve
883:Flat folding
746:
724:
714:Bibliography
679:
673:
654:
648:
621:
615:
607:the original
602:
593:
574:
537:
530:
519:. Retrieved
515:
492:. Retrieved
488:
479:
454:
438:
430:
426:
404:90 degrees (
397:60 degrees (
382:
367:
353:
348:
344:
340:
336:
330:
319:
290:Heinz Strobl
274:Robert Neale
271:
268:
255:Robert Neale
252:
241:
236:
230:
228:
223:
219:
217:
210:
206:
204:
196:
180:
178:
174:
170:
144:unit origami
143:
139:
138:
82:
62:
53:
34:
1229:KĹŤryĹŤ Miura
1224:Jun Maekawa
1199:KĂ´di Husimi
915:Map folding
743:Tomoko Fuse
721:Tomoko Fuse
466:icosahedron
364:Tomoko Fuse
333:Tomoko Fuse
278:Tomoko Fuse
133:icosahedron
110:Tomoko Fuse
85:Icosahedron
48:introducing
1265:Modularity
1259:Categories
1219:Anna Lubiw
1052:Common net
977:Miura fold
756:0870409786
521:2024-07-15
494:2024-07-15
462:bipyramids
358:, such as
248:Joss paper
212:tamatebako
31:references
1137:Origamics
1016:Polyhedra
698:cite book
557:232922105
351:(2018).
335:'s books
130:stellated
1194:Tom Hull
1164:Yan Chen
1047:Blooming
951:Flexagon
785:Archived
745:(1998).
723:(1990).
640:20372390
413:pentagon
399:triangle
356:fractals
339:(1989),
322:polygons
286:Tom Hull
237:kusudama
232:kusudama
198:kusudama
56:May 2009
1270:Origami
441:rhombic
433:pyramid
420:hexagon
187:History
44:improve
1147:People
1002:Sonobe
753:
731:
686:
661:
638:
628:
581:
555:
545:
406:square
389:vertex
343:(1998)
300:, and
167:units.
165:Sonobe
33:, but
308:Types
224:menko
751:ISBN
729:ISBN
704:link
684:ISBN
659:ISBN
636:OCLC
626:ISBN
579:ISBN
553:OCLC
543:ISBN
347:and
181:type
1042:Net
142:or
1261::
1034:,
700:}}
696:{{
634:.
601:.
565:^
551:.
514:.
503:^
487:.
447:.
370:.
304:.
296:,
292:,
288:,
284:,
280:,
250:.
195:A
128:A
1038:)
1030:(
868:e
861:t
854:v
759:.
737:.
706:)
692:.
667:.
642:.
587:.
559:.
524:.
497:.
422:)
415:)
408:)
401:)
345:,
112:.
92:)
69:)
63:(
58:)
54:(
40:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
