Table Of ContentOrnamental Origami
Ornamental Origami
Exploring 3D Geomentric Designs
Meenakshi Mukerji
Boca Raton London New York
CRC Press is an imprint of the
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AN A K PETERS BOOK
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ISBN-13: 978-1-56881-445-2 (pbk)
ISBN-13: 978-1-138-44231-3 (hbk)
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Library of Congress Cataloging-in-Publication Data
Mukerji, Meenakshi, 1962–
Ornamental origami : exploring 3D geometric
designs / Meenakshi Mukerji.
p. cm.
Includes bibliographical references.
ISBN 978-1-56881-445-2 (alk. paper)
1. Origami. 2. Geometry in art. 3. Decoration and
ornament. I. Title.
TT870.M822 2008
736’.982--dc22
2008060660
Cover Photographs
Front cover: QRSTUVWXYZ Stars
Back cover: Flowered Sonobe (top) and Icosahedron
with Curves and Waves (bottom).
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
To my family, Pinaki, Ratul, and Rohit
Contents
Preface vii
Acknowledgments viii
Photo Credits viii
1 (cid:148) Modular Origami Basics 1
Folding Tips and Tools 2
Origami Symbols and Bases 4
Modular Origami and Mathematics 7
Platonic and Archimedean Solids 8
Even Color Distribution 10
2 (cid:148) Windmill Base Models (Created October 2006) 13
Sunburst 14
Starburst 17
Ixora 20
Tuberose 22
Oleander 24
3 (cid:148) Blintz Base Bouquets (Created May 2004) 29
Basic Blintz Unit 30
Impatient 34
Impatient Trillium Bouquet 35
Impatient Gypsophila Bouquet 37
Chrysanthemum and Bouquets 39
Periwinkle and Bouquets 41
Blintz Base Models Without Inserts 43
4 (cid:148) Decorative Icosahedra (Created 2006–2008) 47
Icosahedron with Curves 48
Icosahedron with Curves 2 52
Icosahedron with Curves and Waves 54
Icosahedron with Curves and Petals 56
Patterned Icosahedron 58
5 (cid:148) Embellished Sonobes (Created 2006–2007) 63
Sonobe with Fins 64
Flowered Sonobe 66
Dahlia 70
Geranium 74
Zinnia 79
6 (cid:148) Embellished Floral Balls (Created 2006–2008) 83
Daylily 84
Waterlily 87
Layered Poinsettia 91
Contents vii
Daisy 95
Layered Passion Flower 97
Layered Petunia 99
Dianthus 101
Hexagonal Ornaments 103
7 (cid:148) Planars (Created 2002–2003) 105
History of Planar Models 106
UVWXYZ Rectangles 111
TUVWXYZ Stars 114
TUVWXYZ Rectangles 117
TUVWXYZ Hexagons 119
STUVWXYZ Stars 120
STUVWXYZ Rectangles 123
STUVWXYZ Heptagons 125
RSTUVWXYZ Stars 126
RSTUVWXYZ Rectangles 128
QRSTUVWXYZ Stars 130
Mathematics of Planar Models 132
Aft erword 139
Exercises 139
Bibliography and Suggested Reading 141
Suggested Websites 143
viii Contents
Preface
I greatly enjoyed writing my fi rst book Marvelous origami models. Th e planar model designs use a
Modular Origami (2006, A K Peters, Ltd.). I was moderate amount of mathematics, some of which
not intending to write another so soon; although I has been described in the chapter. A brief history
had a deluge of new origami designs fl ooding my and an exhaustive list of all planar models known
mind by the time I had fi nished my fi rst book. But to date, as compiled by renowned origami artist
so many readers inquired about a next book, that I David Petty, has also been included. Some math-
was greatly motivated to author another. Here is ematical exercises have been provided at the con-
the product of my imagination and your generous clusion of the book for those who would like to
encouragement. test their memory of any high school level math-
ematics.
I learned a great deal from my fi rst writing at-
tempt and this book defi nitely reaps the benefi ts, Diagramming origami models is a bittersweet ex-
now that I am not a novice author. Th is includes perience. Some units that are quite simple and may
a better understanding of what makes an eff ective be taught easily in minutes in a face-to-face meet-
diagram, improved photography, greater atten- ing can take hours to diagram. Easy moves may be
tion to details, and an increased passion for doing diffi cult to illustrate using abstract diagrammatic
a meticulous job overall. Th ere are over 40 new methods. However, at the end of drawing a suc-
models and lots of hints and clues for the folder, cessful diagram there undoubtedly is great satis-
so you can make models that are wholly your own, faction and the “wrist-wrenching” experience of
or variations. For the mathematics lover, I have working the computer mouse extensively seems
included the mathematical aspects of the design well worth the eff ort. A measure of any good ori-
process, wherever possible. gami diagram is that it should have practically no
need for language. Th e universal international
Th e fi rst chapter deals with origami basics and
origami folding symbols that have evolved over
other material that has some overlap with Mar-
time almost prove the language independence of
velous Modular Origami. Without this material,
this art. One can fold from diagrams explained in
a modular origami book is perhaps not complete.
any language without having an iota of knowledge
In addition to origami symbols and bases, I have
about the language itself. Th at is the beauty of the
provided polyhedron charts and color distribution
language of origami symbols.
charts for reference during the assembly phase.
Folding tips along with other matter important to Th is book presents a combination of simple to
folding origami, particularly modular origami, has high intermediate models with an emphasis on the
been provided. Th e relationship between modu- latter and should appeal to a wide range of audi-
lar origami and mathematics has been discussed ences 12 years and older, with or without a math-
as well. ematical background. I hope that you will enjoy
this book as much as my previous one, if not more,
We start with simple models using windmill bases
and spread the joy of origami.
and blintz bases and then gradually progress into
more intricate models such as the decorative ico-
Cupertino, California
sahedra, the embellished Sonobe, and fl oral ball
models, and conclude with a chapter on planar February 2008
Preface ix
Acknowledgments Photo Credits
Th is book would not have been possible without (In rough order of appearance)
the encouragement that so many people have pro-
vided me and I would like to thank each and every • Bonefolder (page 3): Photo by Christine Cox
one of them. Additionally, there are many people of Volcano Arts http://www.volcanoarts.biz
who have assisted me with the book by making • Chrysanthemum/Trillium (page 28) and
direct or indirect contributions, and I will try my Impatient/Gypsophila (page 45): Fold-
best to thank them one by one, hoping not to miss ing and photos by Aldo Marcell Velásquez
anybody. First of all, I would like to thank Da- (Nicaragua).
vid Petty for contributing to the chapter on pla-
• Impatient (page 34) and 12-unit Chrysanthe-
nar models a comprehensive history and a com-
mum/Gypsophila (page 40): Folding by child
plete list of existing planar models including their
artist Anjali Pemmaraju (California).
fi nished model drawings. Next, I would like to
thank Bennett Arnstein and Rona Gurkewitz for • Icosahedron with Curves 2 (pages 46 and
granting me permission to use their Triangle Edge 53): Folding by child artist Smriti Pramanick
Module [Gur95] in my Decorative Icosahedra (California).
chapter. Th anks to all those who have meticulous-
• Flowered Sonobe and Geranium (page 62),
ly test folded, especially Rosalinda Sanchez, Halina
Dahlia Variation (page 73), Geranium Varia-
Rosciszewska-Narloch, Rachel Katz, Aldo Marcell
tion (page 78), Layered Petunia (page 82), and
Velásquez, and Anne LaVin. No diagram is com-
Daylily (page 86, top): Folding by Halina Ro-
plete until test folded by somebody other than the
sciszewska-Narloch (Poland) and photos by
author. I’d also like to thank Halina and Rosalinda
Sebastian Janas (Poland).
for adding special eff ects to some of my photos.
• TUVWXYZ Stars (page 104): Folding and
Th anks to Jean Jaiswal for proofreading all the text
photo by Rosalinda Sanchez (Arizona).
and for her enthusiasm. Th anks to Robert Lang
for always being there to answer the various ques- • UVWXYZ Rectangles (page 113), STU-
tions that I have had from time to time. Th anks to VWXYZ Rectangles (page 124), and RTU-
the Singhal family for their continued inspiration. VWXYZ Stars (page 127): Folding and photos
Th anks to my publisher A K Peters, Ltd. for their by Matt Johnston (Washington).
tireless teamwork that refi ned my book. Th anks to
• TUVWXYZ Rectangles (page 118) and STU-
all those who have folded models and contributed
VWXYZ Stars (page 122): Folding and photos
beautiful photographs. Th ey have been acknowl-
by André Bracchi (France).
edged separately in the Photo Credits section.
• All other folding and photos are by the
Th anks to David Lister, Th omas Hull, Paul Jack-
author.
son, and Boaz Shuval for being readily available
for consulting. Th anks to the numerous viewers
of my website for providing constant encourage-
ment. And fi nally, hearty thanks to my husband
Pinaki, and sons Ratul and Rohit, for proofreading
and providing all kinds of support and for simply
being there.
x Acknowledgments
