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E-grāmata: Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design 2nd edition [Taylor & Francis e-book]

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This new edition of Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design introduces an innovative pleat pattern technique for origami designs that is easily accessible to anyone who enjoys the geometry of paper. The book begins with six basic forms meant to ease the reader into the style, and then systematically scaffolds the instructions to build a strong understanding of the techniques, leading to instructions on a limitless number of patterns. It then describes a process of designing additional building blocks. At the end, what emerges is a fascinating artform that will enrich folders for many years. Unlike standard, project-based origami books, Six Simple Twists focuses on how to design, rather than construct.

In this thoroughly updated second edition, the book explores new techniques and example tessellations, with full-page images, and mathematical analysis of the patterns. A reader will, through practice, gain the ability to create still more complex and fascinating designs.

Key Features











Introduces the reader to origami tessellations and demonstrates their place in the origami community





New layout and instructional approach restructure the book from the ground up







Addresses common tessellation questions, such as what types of paper are best to use, and how this artform rose in popularity





Teaches the reader how to grid a sheet of paper and the importance of the pre-creases





Gives the reader the ability to create and understand tessellations through scaffolded instruction





Includes exercises to test understanding





Introduces a new notation system for precisely describing pleat intersections







Analyzes pleat intersections mathematically using geometrically-focused models, including information about Brocard points
Preface vii
Acknowledgments ix
About the Author xi
1 Why Study Pleat Patterns?
1(52)
1.1 Basics and Preparation
2(1)
1.2 How Pleat Patterns Differ from Traditional Origami
3(1)
1.3 Fold Parity and How to Read the Diagrams
4(2)
1.4 Folding Uniform Parallel Creases
6(8)
1.5 Grid Axes and How to Fold a Hexagon
14(7)
1.6 How to Fold a Triangle Grid
21(7)
1.7 Simple Pleat
28(5)
1.8 The Six Simple Twists
33(1)
1.9 Triangle Twist
34(2)
1.10 Triangle Spread Twist
36(1)
1.11 Hex Twist
37(4)
1.12 Hex Spread Twist
41(1)
1.13 Rhombic Twist
42(3)
1.14 Arrow Twist
45(3)
1.15 Anatomy of a Molecule
48(1)
1.16 Pleat Intersection Notation
49(4)
2 How to Use the Six Simple Twists
53(142)
2.1 32nds Grid
54(2)
2.2 Locking and Unlocking Pleats
56(3)
2.3 Triangle Twist Tessellation
59(4)
2.4 Hexagon and Triangle Twist Tessellation
63(5)
2.5 Tessellation Basics (without Folding)
68(5)
2.6 Applying Tessellation Knowledge to Folding
73(1)
2.7 Triangle Weave Pattern
74(4)
2.8 The Hex Weave Pattern
78(5)
2.9 Hexagonal Failed Cluster
83(3)
2.10 Modifications
86(5)
2.11 Backtwisting
91(3)
2.12 Twist Handedness and Pleat Symmetry
94(1)
2.13 Pleat Flattening
95(5)
2.14 Triangle Twist Tessellation with Flattened Pleats
100(5)
2.15 Hidden Circles Pattern
105(3)
2.16 Rhombic Twist Tessellation
108(4)
2.17 Rhombic Twist Variants
112(2)
2.18 Twist Sinking
114(3)
2.19 Twist Expansion
117(3)
2.20 Nub Offset Tessellation
120(7)
2.21 Shift Rosette Tessellation
127(7)
2.22 Ridge Creation
134(4)
2.23 Button Molecule
138(1)
2.24 Button Molecule Tessellation
139(4)
2.25 Triangle Flagstone Tessellation and Offsetting Pleats
143(4)
2.26 3.6.3.6 Flagstone Tessellation
147(6)
2.27 Crooked Split
153(5)
2.28 Snowflake Tessellation
158(2)
2.29 Tulip Split
160(3)
2.30 Tulip Split Tessellation
163(2)
2.31 Molecule Size and Different Grid Densities
165(11)
2.32 "Front" and "Reverse" Sides
176(2)
2.33 Tendril Tessellation
178(3)
2.34 Inverting a Pleat
181(3)
2.35 Iso-Area Triangle Twist Tessellation
184(5)
2.36 Pleat Pushing and the Platform Tessellation
189(3)
2.37 Triple Twist Tessellation
192(3)
3 Pleat Patterns as Artwork
195(100)
3.1 Gallery
196(13)
3.2 Pleat-to-Molecule Analysis
209(1)
3.3 Pleat Intersection Archetype Sets
209(3)
3.4 Molecule Database
212(21)
3.5 Archetype Composition
233(7)
3.6 Actions and Notations
240(7)
3.7 Splitting Equation
247(11)
3.8 The Normal Polygon
258(4)
3.9 The Circle Cutout Model
262(4)
3.10 Molecule-to-Pleat Analysis
266(4)
3.11 Sectioning Method of Twist Design
270(16)
3.12 Brocard Points and the Shutter Skeleton of a Polygon
286(9)
4 Final Thoughts 2.0
295(1)
Pleat Notation Thoughts 296(1)
Terminology 297(4)
Glossary 301(5)
Photography Credit 306
Born in Pittsburgh and living in Connecticut, Benjamin DiLeonardo-Parker has an active student of origami tessellations since 2007. He has taught and exhibited at origami conventions and art shows internationally, including Chi Mei Museum (Tainan City, Taiwan), La Escuela-Museo Origami de Zaragosa (Zaragosa, Spain), The Science Museum Oklahoma (Oklahoma City, OK), the Museum of Mathematics (New York, NY), the Japan Information and Culture Center (Washington D.C.), The New Britain Museum of American Art (New Britain, CT), and the Cooper Union Gallery (New York, NY).

Outside of art, Ben teaches high school mathematics to students with uncommon learning styles, and incorporates origami into his classes as often as he can. Ben approaches his artwork from a holistic standpoint, preferring to view origami as an entry into the vast network of disciplines to which it is connected. This has led him to extend his knowledge of education, engineering, mathematics, CNC fabrication, paper arts, fashion, alternative photography, and other studies. When not teaching high school math, Ben operates a workshop in Essex, CT out of which he creates artwork and runs classes on origami design,

He views his practice of origami as cyclical and recursive. Origami is connected to such as vast network of disciplines, each with its own sirens call. Each flavor, each culture, cycles back onto its own basics over and over, swirling and interacting with previous knowledge, each enhancing the others in some way.