Origami Tessellations. Awe-Inspiring Geometric Designs.pdf

Open-Back Square Twist ................................. 21

Open-Back Hexagon Twist ...................... ..... ... 22

BEGINNER PROJECiS

Five-and-Four .......................................... ..... 24

Spread Hexagons.......... .. ............. ........ ... .... . 28

Tiled Hexagons ............................................ 32

Star Puff. ................ ........................... ........... 36

3.6.3.6 ................. ... .. ................ ... ...... ........... 4()

Pinwheel ............ .... .... ................................... 43

Open-Back Hexagon Twist.. ........................ 47

Basket Weave ... ...... .... ................................. 50

Water Bomb ...... ...... .................................... 54

Square Weave ...... ...................................... .. 51

INTERMEDIATE PROJECTS

Contents

Chateau-Chinon .......................................... 6()

Rhombus Weave .............. ..................... .. .... 64

Preface ..................... ..... .. ................... .. ....... ........ \fI

Roman Church Floor Tiling .... ............ ......... 70

Overview ........ .. ............... .. .... ............................... 2

Daisy Chains ................ ..... .......... ............... ... 73

Double Triangle Sawtooth ............ .... ......... 76

Stacked Triangles ........................................ SO

Bird Base .......... ........ ........... .... ....... ............. . 84

Propellerheads ....................... .. ................... 88

Techniques .. .. ......................... ............................... 5

Precreasing ..................................... ................. .. 5

Sq~are Grid .. ........... ........ ..... .. .... ....... ........ ....... e,

Triangle Grid ..................................................... 7

r Pleat Intersections .. .. .. ............ .. ....................... 9

120-Degree Pleat Intersection ........................... 9 ADVANCED PROJECTS ------

120-Degree Inverted Pleat Intersection ............ U) Arabesque Flourish .. .......... ................ ......... 92

gO-Degree Pleat Intersection ............................ 11 Field of Stars ............................................... 96

60-Degree Pleat Intersection ........................... 12 Negative Space Stars ................... .. ............. 99

Rabbit-Ear Triangle Sink ................................... 14 3.4.6.4 ......................................................... 1()3

Twists ....... ..................................... ....... ... ......... 16 Aztec Twist ................................................ 106

Triangle Twist .................................................. 1(, Arms of Sh iva ............................................. 110

Square Twist ............... .. .......... ...... .... .. ............ 17 Gallery .............................................................. 114

Hexagon Twist .......... .. .................................... 18 Acknowledgments... .... .. ... ... .. ... ......... ... ... ........ 12()

Rhombus Twist........ ....................................... 20 About the Author .... .... ..... ... ... .. ........ ............... 120

Open-Back Triangle Twist ................................ 21

Index ..... .............................................. ............... 121

Star Twist.................. .................... ...... .... ..... e,7

..,hen I was five, my parents asked me what I wanted

n to be when I grew up. "A paperologist," I replied

enthusiastically.

Throughout my early childhood and teen years,

I enjoyed paper crafts and origami. I found imagining

a thing and then creating it from materials at hand very

satisfying. Friends and family frequently gave me stacks

of papers and rolls of tape as birthday gifts.

Paperology wasn't a major at my college of choice,

however. So, after preparing for a technology career,

I found I still needed an artistic outlet. I turned back to

my childhood love of paper and origami .

How was I drawn to the geometric art of origami

tessellations, specifically? It started with a fish .

I was folding an origami koi designed by Robert J.

Lang . The fish-scale design was folded from repeated

patterns called tessellations . I practiced a bit on some scraps

of paper, and, just like a fish, I was hooked on tessella-

tions . I folded sheet after sheet of paper, experimenting

with different shapes and variations . My excitement led

to deeper exploration and the creation of new tessellation

designs . I never looked back; in fact, I never did complete

that fish!

Since then I have folded hundreds of origami tessella-

t ions . Tessellations are geometric patterns that can repeat

forever. When captured in paper, beautiful pieces of art are

created in intricate pleats and folds .

For this book, I have taken 25 of my favorite tessel-

lations and turned them into projects for newcomers and

experienced origamists alike . With step-by-step instructions,

illustrated crease patterns, and how-to photos, you'll learn

to create these wonderful designs yourself-hopefully,

more easily than I did!

This book covers the fundamentals of origami tessella-

tions, providing a little history and describing simple begin-

ning techniques with detailed illustrations. The techniques

then are utilized in specific projects that will help you make

impressive works of art. Finally, the book's gallery of tessel -

lation images is designed to inspire you to experiment and

innovate, trying out the tessellations of others and, eventu -

ally, creating your own patterns.

NO ClJiilNG, NO GI.lJING,

ON I: Stll: I:i 01: I'J.\I'I: It

All you need to make origami tessellations are your two

hands and a piece of paper. Folding tessellations is not

complicated. At its core, it is the repetition of simple folding

patterns to create larger, more complex designs .

Folding tessellations is a meditative experience . While

origami is labor-intensive, it's also very relaxing . Often

when I fold something I lose track of time. Hours pass

without my knowledge. When I'm finished, the completed

piece is almost like a present.

When I teach students how to create tessellations, they

always have an "Aha!" moment. They suddenly, unexpect-

edly understand how the folded shapes repeat themselves

and how they all work together. From that point on the

students take off and start folding madly. Three words of

warning: Tessellations are addictive!

Don't worry if your first project comes out imperfectly;

your next attempt will be greatly improved . Your own

"Aha!" moment will come soon. Practice and repetition are

great teachers .

As your skill and experience increase, you 'll start to see

tessellation patterns everywhere. Tiles on the floor, cobble-

stones in the courtyard, the patterns of light falling through a

stained-glass window-you'll find inspiration all around you .

You may find discovery and creation are the most

rewarding parts of this craft, because making origami

tessellations is very much about infinite possibility. When

you draw upon your newfound recognition of patterns and

think about how they might be recreated in paper, you can

use the techniques in this book to create amazing arrange-

ments and artwork all your own.

INiIIOI)IJCiION

,\NI) il:CtINIQIJI:S

The tiles you saw likely created tessellations-repeating

patterns of specific shapes . The word "tessellation"

comes from the Latin tessel/a, meaning "small square ."

The Romans frequently used squares for making mosaics

and tile designs .

While the Romans and Byzantines made complex

mosaic patterns, tessellations were raised to a true art form

by artisans of the Islamic faith . Since Islam forbade repre-

sentational imagery, artists and craftsmen focused their

creativity on developing complex geometric designs. Their

geometric orientation was reflected in inspiring architec-

ture, tile work, painting, ceramics, and illustration.

The Islamic Moors in Spain built the Alhambra, a

magnificent palace decorated with some of the best tessel-

lation artwork in the world. The Dutch artist M . C. Escher

(1898-1972) made several visits to the Alhambra . The

complex tessellation patterns he studied had a formative

impact on his art. Escher said the tiling at the Alhambra

was "the richest source of inspiration I have ever tapped ."

Now Escher's own art is among the most widely

known and loved in the world. Tessellations are an impor-

tant part of many of his sketches and illustrations, which

feature fantastic animals, figures, and shapes .

Tessellating Birds by David Bailey

Today's origami tessellations are primarily the brain-

child of Shuzo Fujimoto, a Japanese chemistry teacher who

was instrumental in exploring the possibilities of folding

repeating shapes on paper. Fujimoto's singular focus on

origami tessellations continues to inspire many folders .

Most of the basic tessellation ideas covered in this book

were discovered by Fujimoto-sensei in the 1970s.

Many people have contributed to this art form's

development, including the computer scientist Ron Resch,

prolific origami author Yoshihide Momotani, and artist

Chris Palmer. Not long after spending six months living in

the caves of Sacremonte outside of Granada, Spain, on an

artistic journey to study the tilings of the Alhambra, Palmer

was exposed to the tessellations of Fujimoto.

Building on Fujimoto's work, Palmer has pushed the art

of origami tessellations upward and outward. He is one of

the greatest tessellation folders today, and many tessella-

tion artists count Palmer among their primary influences.

OIIlGj.\MI il:SSI:I.I.j.\iIONS

Origami tessellations are geometric designs folded from

a single sheet of paper, creating a repeating pattern of

shapes from folded pleats and twists. Tessellated origami

pieces range from simple square tilings to extremely intri-

cate, complex pieces inspired by Islamic art. Tessellated

shapes can form everything from twisted architectural

flourishes to realistic faces .

",tU\i IS' il:SSI:I.IJ.\iION7

tl ave you ever looked at the patterns on a tile floor?

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