EKATERINA LUKASHEVA MODULAR ORIGAMI
EKATERINA LUKASHEVAMODULAR ORIGAMIKALEIDOSCOPE1
Copyright 2016 by Ekaterina Pavlović (Lukasheva)All rights reserved. No part of this publication may be reproduced, distributed, or transmitted inany form or by any means, including photocopying, recording, or other electronic or mechanicalmethods, without the prior written permission of the publisher, except in the case of brief quotationsembodied in critical reviews and certain other noncommercial uses permitted by copyright law.The designs in the book are intended for personal use only, no commercial use without author’swritten permission. For permission requests or wholesale orders, write to art@kusudama.me.Publisher’s Cataloging-in-Publication dataLukasheva, Ekaterina.Modular origami kaleidoscope / Ekaterina LukashevaISBN-13: 978-0-9973119-4-5ISBN-10: 0-9973119-4-0The origami models in this book were created by Ekaterina Pavlović (Lukasheva) in the following years:2010: Aristata, Masquerade;2011: Eve, Prima, Tigra, Tiger;2012: Almandine, Chameleon Eye, Delicate Flower, Flower Star, Forma Perfecta;2013: Bicolor, Insignia, Kohleria, Lathyrus, Pulsatilla, Radiant Flower, Secret Flower;2014: Flora, Flora Flower;2015: Clematis, Sprouts, Nerium.Thanks to all the people who helped me make, test fold,proof-read and illustrate this book. Namely:Elena BelogorodtsevaOlga DumerUniya FilonovaEkaterina KimInna LupanovaRosemary Lyndall WemmAlina MaslovaBoris PavlovićTanya TurovaJean Wallaceand all the other people who inspired, encouraged and asked me to write a new book.Photo creditsEkaterina Kim: portrait on the cover.Inna Lupanova: picture on page 38 (top).Alina Maslova - picture on page 51, page 56.Tanya Turova: pictures on page 22, page 26, page 30, page 31, page 35, page 38(bottom), page 39, page 40, page 60, page 50 (bottom), page 64, page 66.Jean Wallace: the diagrams on page 60, page 48.2
CONTENTS681010111213141516161718Origami SymbolsCutting RectanglesWhat is Modular OrigamiAbout the AuthorModular AssemblyOctahedron (12A)Cube (12B)Icosahedron (30A)Dodecahedron (30B)Assembly HintTips and TricksBook SymbolsModelsDelicate Flowerpage 20Clematispage 32Flower Starpage 18Aristata Transformerpage 42Tigrapage 48Almandinepage 22Forma Perfecta var.2page 38Chameleon Eye var.1page 30Aristatapage 403
4Tigrapage 48Chameleon Eyepage 27Bicolor variationpage 26Tiger variationpage 53Forma Perfecta var.3page 39Florapage 44Bicolorpage 24Tigerpage 51Forma Perfecta var.2page 38Pulsatillapage 64Primapage 54Kohleriapage 56
Flora Flowerpage 46Insigniapage 58Secret Flowerpage 60Secret Flower variationpage 63Masqueradepage 71Radiant Flowerpage 66Evepage 68Masqueradepage 71Floral Masqueradepage 75Sproutspage 76Neriumpage 78Lathyruspage 795
ORIGAMI SYMBOLSvalley foldmountain foldvalley fold and unfoldmountain fold and unfoldequal lengths6pleat foldequal anglesunfoldunfold/pull paper
enlarged view aheadcurlsink foldinside reverse foldback (hidden) layerrepeat on the other side90 90 90 rotate 90 (or any other angle if specified)90 turn paper over90 semi-fold (pre-crease)put inside7
HOW TO CUT A.1:2 RECTANGLE (HALF SQUARE)121: 3 RECTANGLE213434 the lower rectangle1: 2 RECTANGLE1 start with squareor rectangle82has 1: 2 proportion
DIVISION INTO THIRDS123USING A TEMPLATE4 make the creaseparallel to the sidethrough the intersection, then makethe second creaseUse the following method to divide a square into thirds in order to save time and avoid unnecessary creases.Divide the first square into thirds by using the above method and use it as a template for the other units.1 to make the templatedo steps 1-4 of theabove method2 insert the other square of3 make the crease on the new squarethe same size till the endto the templateto the paper border; the new creasewill be exactly 1/3 of the square2:3 RECTANGLE1 start with step 4 ofdividing to thirds23At step 1, the gray partis equal to 2/3 of thesquare’s length, and thewhite part is equal to 1/3.If you want a large 2:3rectangle, cut the whitepart away at this step anduse the remaining grayarea. If you wish to havesmaller 2:3 rectangles,continue to steps 2-3.9
MODULAR ORIGAMIOrigami is the art of paper folding.Traditional origami uses a single, uncut sheetof paper, whereas modular origami usesmultiple sheets joined together to create asingle form. This method offers great flexibility,while keeping the single unit relativelysimple. So if you dislike 100 step origamidiagrams, but still want the resulting piece tolook intricate, modular origami is for you.The figures created through modularorigami are usually highly symmetric,because they are made from multipleequivalent units, or modules. The origamimodules usually have special locks to allowunit-to‑unit connection without using anyadhesive. This feature of modular origamibrings it closer to construction sets: you arejust making the pieces of the constructionset yourself prior to the assembly process.There are several names for modularorigami throughout the world. In the Westit is referred to as modular origami, butin Eastern Europe and South America,the Japanese word “kusudama” is commonlyused for ball‑like modular origami figures.In Japan, the word “kusudama” originallymeant “medicine ball”, possibly referring to aball made from flowers and used for incense.ABOUT THE AUTHORMy name is Ekaterina Lukasheva, but myfriends call me Kate. I became acquaintedwith modular origami as a teenager; it quicklybecame my passion and has been eversince. As I grew up, I continually developedmy modular origami skills, and at some pointI started creating my own designs. It is veryinteresting, since I compose the puzzles thatI can then assemble into beautiful spheres.When I create a new origami model, I try toeither make it look different from the existingmodels or make its modular locks different.This book is my third published book.Kusudama Origami came out in 2014followed by Modern Kusudama Origamiin 2015. You can find more informationabout my other books on page 82.Besides, I usually publish my diagrams invarious origami journals and conventionbooks throughout the world. You canalso find numerous kusudama pictures as10well as a few free diagrams and videoson my website: www.kusudama.me.I was born in 1986 in Moscow,Russia. Since early childhood I was fondof architecture and design art books andcatalogs, as well as “entertaining math”books. I tried several hobbies throughoutmy life such as construction sets, drawing,painting, photography, modeling and.origami. I am fascinated by the latter at themoment. For me it is the ultimate manifestationof mathematics, art and design. I gaininspiration from various 3-dimensionalobjects like flowers, cacti, architectureobjects and stellated polyhedrons.Even hold a M.Sc. in appliedmath and programming and a PhD indifferential equations, I do not thinkbackground in mathematics is necessaryto make and enjoy beautiful origami. ;)
MODULAR ASSEMBLYThe units presented in this book can be assembled in various ways. Theassembly methods for modular origami spheres are based on the structureof Platonic1 and Archimedean2 solids. Each unit corresponds to an edge ofthe solid. The detailed assembly of these solids is outlined below.There are two types of units in this book: ‘edge’ units and ‘solid’ units. Theformer act and look like real edges of the solids when you assemble the modules.But indeed the ‘solid’ units act in the same way: the only difference is that the finalshape becomes solid, and the holes between the units turn into pyramids.edge unitssolid unitsIt means that the same assembly methods can be used for both ‘types’ of units.The following image illustrates the correspondence between units and the underlying sedgeverticesThe methods below will illustrate the assembly methods for the edge units. But thesame assembly schemes apply to the solid units as well. The assembly schemes aregiven symbolically, each arrow represents the unit’s particular connection method.1 A Platonic solid is a regular convex polyhedron composed of identical regular polygons meeting at identical vertices.2 An Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of twoor more types of regular polygons meeting at identical vertices. They are distinct from the Platonic solids, which are composed of only one type of polygon meeting at identical vertices.11
OCTAHEDRONmethod 12AA regular octahedron is a Platonic solid composed of 8 equilateral triangles, 4 of which meet at each vertex. Sincean octahedron is formed with 12 edges, you will need 12 units to complete a modular octahedron figure.connect 4 units so thatthey meet at a single pointcontinue adding the units so that every 3 units form atriangular hole (triangular pyramid in case of solid units)complete octahedronadd 4 more units so that 4units meet at a single point each timeconnect the sides marked with thestars in the illustration to a single pointbehind, completing the octahedronthe solid version of the octahedron: the dottedlines show the underlying octahedron12
CUBEmethod 12BA regular cube is a Platonic solid composed of 6 square faces, with3 edges meeting at each vertex. Since a cube is formed with 12edges, you will need 12 units to complete a modular cube figure.connect 3 units so that theymeet at a single pointconnect loose units as showncomplete cubeadd units to the loose sides of the edges sothat 3 units meet at a single point each timeadd the remaining units so that 3 units meet ata single vertex, connect the sides of the unitsmarked with triangles to a single point behindthe solid version of the complete cube: thedotted line shows the underlying cube13
ICOSAHEDRONmethod 30AAn icosahedron is a polyhedron composed of 20 triangular faces, with 5 of those meeting at each vertex.Since an icosahedron is formed with 30 edges, you will need 30 units to complete a modular icosahedron figure.connect 5 units so thatthey meet at a single pointadd 5 more units toform 5 trianglesconnect the loose sides of the unitsso that they form 5 trianglesadd units to thenon-finished vertices so that5 units meet at a single point;the units marked with the stars in thepicture should meet at a single pointconnect 2 additional units to everyunfinished vertex, so that 5 units meet ata single vertex each timethe complete icosahedron (left)and the solid version of theicosahedron (right)the size of the holes, as well asthe sharpness of the spikes, mayvary from unit to unit14
DODECAHEDRONmethod 30BA dodecahedron is a Platonic solid composed of 12 pentagonal faces, with 3 of those meeting at each vertex. Sincea dodecahedron is formed with 30 edges, you will need 30 units to complete a modular dodecahedron figure. Theassembly scheme described below may not be the most comfortable; while it illustrates the algorithm, the actual sequenceof the assembly may be slightly different.5554connect 5 units so that theyform a ring1add 2 units to every loose sideof the unit so that 3 units meetat every pointconnect 5 more units so thatevery 3 units meet at a singlevertex as shown211!252!45335354add 5 more units sothat every 3 units meet at a singlepoint, then make a new ring of unitsthe same way you did in the first step4connect the loose edges sothat you get 5 pentagonal ringsaround the central oneconnect this new ring to the figure so thatthe numbers in the grey pentagons match up4this picture is to illustrate the structure only,as it is easier to add the last 5units one by onethe complete dodecahedron (left)and the solid version ofdodecahedron (right)the size of the holes as well as thesharpness of the spikes may varyfrom unit to unit15
ASSEMBLY HINTSome of the models in this book sharethe polyhedron first. Thus, when you assemblea similar connection system which can lookan icosahedron, finish the vertices where fiveunstable at first glance. However, if you joinedges are connected. Since a “star” of fiveunits is enclosed it becomes stable (steps 1-5the pieces as shown below, they will connectmore stable, and assembly process willin the picture). Instead of closing the adjacentbe more comfortable. The diagram belowtriangles, you should then assemble theillustrates the modified assembly sequencenext “star” (steps 6-10). Continue tofor the icosahedron (30A method), but theassemble the model by finishing the vertices,How to assemble units:proceeding in this fashion until the model issame idea may be applied to any spherethe connection becomes stable when it’s connected to the closed ”star”.finished. As you go, keep in mind that theyou assemble. The concept behind thisClose the circle from first 5 units and then arrange the second star neat the first.method is to try and finish the vertices ofholes between the units should be triangular.17256843109TIPS AND TRICKSContinue adding units so that each five meet at one pointand the windows between the units are triangles. You will need 30 units.youtoassemblemodularvertices IfTrychooseotherpapersof theformssame(below)type you should Ifassembleyou are completenot sure howto perform ato make them stable.and weight for a single model. If youparticular step, refer to the next step inmix papers with different properties inthe diagram, as the illustration shoulda single model it may not only lookgive you a hint of the resulting shape.inconsistent but may also lack symmetry. If you would like to use sticky notes for Try folding a test unit from lager piece offolding , you can apply some cornpaper before starting the entire modular.starch directly on the adhesive, makingIt may give you a hint as to what paperit less sticky and more ideal for folding.size would be most comfortable for you, Be as accurate as possible when makas well as how the color or pattern ofing every single unit. The more precisethe paper will appear when folded intoyou are, the better the final model willa particular module.look. Somemodular locks only function12 units30 unitswhen your folding is very precise.16
A pincer or tweezers can bevery handy during the assemblyprocess or for curling the petals.Use it when you need to tuck thesmall flaps into pockets.For precise and sharper creasesuse a folder or a wooden stick.You may find a special origamifolder or use some clay modelingtools you can find in any artsupply store.Paper and craft knivescan be used for cuttingpaper.A letter opener can bevery useful for cutting paperwhen you travel; you cantake it even on board!Clips can be helpful totemporarily fasten the units forstability during the assembly.PVA glueThe models in the book do not generally require glue for assembly, but if you are a novice to modular origamiyou may need some. If you want your kusudama have a better chance of staying together when handled byguests, children or gently batted by animals, add a bit or glue during assembly or to a complete model. Stick glueis better during assembly, while PVA glue (white liquid glue) can be used to fasten more permanently the completemodel. Add a drop of PVA glue to the point where units meet to fasten the point. This glue becomes nearlyinvisible when dry, but be sure to test it on a scrap of your selected paper before adding to the kusudama.Near the model name for each diagram in this book, you will find some symbols and other indicators withsuggestions to help guide you in your paper selection, as well as the difficulty level and assembly possibilities fora particular model.Suggests the use oforigami-specificgradient paper: thereare several types ofdifferent patterns, specificpattern can enhance model a lot.Suggests the use of paperwith different colors oneach side.The other side of thepaper won’t be seen.30A, 12ADifficulty level out of 5.Recommended assemblymethod and number ofunits (see pages 12-15).7x7 cm squareRecommended paper size(novices may want to use largerpaper, whereas experiencedfolders could go even smaller).MODEL NAME17
5 units5 x 7.1 cm rectangle (proportion 1: 2 (1:1.41))FLOWER STARThis is a good starting model, because itonly requires 5 units to form a star.You can use cutting instructions fromthe beginning of the bookor use European letter paper(which has the same 1: 2proportion) and divide it into16 equal rectangles.1 start with 1: 2 rectangle,see page 8 for cutting instructions1823 fold aligning the points
45 fold simultaneously678 inside reverse fold9(for the perfect result you can lockthe tiny flap inside with the layerof paper you folded at step 4)flap10 semi-foldcomplete unitto connect the units, slide thepetal under the flapthis connection will become stableonly when you complete the starpush to the sides of the starduring the assembly to helpthe units stay togetheradd 3 more units tocomplete the starshape and curl thepetals for better look19
4-6 units5 x 10 cm rectangle (proportion 1:2)DELICATEFLOWER1 start with 1:2 rectangle,see page 8 for cutting instructions2023 fold aligning the points
45 cut along the crease67 fold simultaneously89 fold along the trisector so that101112you made in step 4the white part lies equallybetween the color sections;if you’re having trouble,see the next pictureplace forthe flapflap13 semi-foldcomplete unitto connect the units slidethe petal under the flapthis connection willbecome stable only whenyou complete the starpush to the sides of the starduring the assembly to helpthe units stay together;add 3 more units and thencomplete the star;shape and curl the petalsfor better look21
30A, 12A7 x 7 cm squareALMANDINEThis model can have two different faces. If youchoose harmony paper, you can accent the flowerlike petals. If you chose monotone paper, you willemphasize the unusual geometry of this model.30A22123456 inside reverse fold
45 45 7891011 repeat steps 9-10and unfold12 semi-fold along themarked linespocketflapcomplete unit2 connected units: add the 3rd unit to make a triangularpyramid with the hole in the centerif you’re having trouble, see the next pictureto connect the units slide theflap into the pocket3 connected unitsuse assembly method 30A on page 14or assembly method 12A on page 1223
30A, 12A6 x 9 cm rectangle (proportion 2:3)BICOLORThis is sample pdf.You can learn more about the book contents athttp://books.kusudama.me/You can buy the book athttp://www.amazon.com/dp/0997311940To contact me use art@kusudama.me30A1 start with 2:3 rectangle,see page 9 for cutting instructions242
Kusudama Origami came out in 2014 followed by Modern Kusudama Origami in 2015. You can find more information about my other books on page 82. Besides, I usually publish my diagrams in various origami journals and convention books throughout the world. You can also find numerous ku
3 6 origami symbols 8 cutting rectangles 10 what is modular origami 10 about the author 11 modular assembly 12 octahedron (12A) 13 cube (12B) 14 icosahedron (30A) 15 dodecahedron (30B) 16 assembly hint 16 tips and tricks 17 book symbols 18 models CONTENTS page 28 page 24 page 42 page 43 page 18 page 20 page 32 page 53
Origami is a paper folding art that emerged in Japan (Yoshioka, 1963). Origami has two types, classical origami and modular origami (Tuğrul & Kavici, 2002). A single piece of paper is used in classic origami. Different items, animal figures and two-dimensional geometric shapes can be made with classic origami.
043-Origami Flowers: Popular Blossoms and Creative Bouquets - Hiromi Hayashi 15,00 044 044-Origami Pop-Ups - Jeremy Shafer 22,00 045 045-Kusudama Origami - Ekaternia Lukasheva 16,00 046 046-Wondrous One Sheet Origami - Menakshi Mukerji 24,00 047 047-Origami Europe Edición blanco y negro - BOS 9,00
Bird Origami Butterfly Origami THE Complete Book of Hummingbirds Disney Classic Crochet Marvel ’s The Avengers Vault Montreal Then and Now Noah ’s Ark Origami Origami Aircraft Origami Chess: Cats vs. Dogs Peanuts Crochet Star Wars Crochet Vancouver Then and Now Spring 2015. AWARD-WINNING TITLES
of rigid-foldable origami into thick panels structure with kinetic mo-tion, which leads to novel designs of origami for various engineering purposes including architecture. 1 Introduction Rigid-foldable origami or rigid origami is a piecewise linear origami that is continuously transformable without the deformation of each facet. There-
but some of the most direct appear in the genre of modular origami. In modular origami, one folds many sheets into identical units (or a few types of unit), and then fits the units together into larger constructions, most often, some polyhedral form. Modular origami is a diverse and dynamic field, with many practitioners (see, e.g., [12, 3]).
- Origami composto, que se obtém por união de vários origami simples; - Origami modular, que consiste num origami composto em que as peças são todas geometricamente iguais. Para efectuar dobragens de papel, existem hoje vários livros de modelos para a construção de algumas figuras. Em todos estes documentos, existe uma simbologia,
Rumki Basu, (2004) Public Administration: Concepts and Theories, Sterling Publication, Delhi. 22. Bhogale Shantaram, (2006) Lokprashasanache Siddhant aani Kaeryapadhati, Kailas Prakashan, Aurangabad. 23. Patil B. B., Public Administration (Marathi), Phadake Prakashan, Kolhapur, 2004. 8 SYLLABUS FOR TYBA POLITICAL SCIENCE (S-4) INTERNATIONAL POLITICS Course Rationale: This paper deals with .
