Star Origami The Starrygami™ Galaxy of Modular Origami Stars, Rings and Wreaths

1 Introduction. 1.1. Stars. 1.2. Origami stars and how this book is organised. 1.3. How to use this book. 1.4. The models. 1.5. Difficulty. 2. Stars. 2.1. Regular polygons. 2.2. Overlapping regular polygons. 2.3. Stellating a regular polygon. 2.4. Joining the diagonals of a regular polygon to make a star polygon. 2.5. Moving midpoints of the edges towards or away from the centre. 2.6. Rosette. 2.7. Kaleidoscope mirrors. 2.8. Taking a shape and rotating it around a centre of rotation. 3. Special Rectangles. 3.1. The square. 3.2. The silver rectangle. 3.3. The leftover rectangle. 3.4. The bronze rectangle. 3.5. The double bronze or half bronze rectangle. 3.6. The golden rectangle. 3.7. The double square or half square. 3.8. The 1:3 rectangle. 3.9. The 4:5 rectangle. 3.10. Landscape-portrait (LP) rectangles. 3.11. Other rectangles. 4. Folding and Generalising Stars. 4.1. Variation and creation. 4.2. Varying and generalising a flat star. 4.3. Varying and generalising a single model. 4.4. Summary. 5. Tips on Paper and Folding. 5.1. Paper. 5.2. Paper colour and patterns. 5.3. Paper size. 5.4. Preparing paper. 5.5. Folding the modules. 5.6. Assembling the modules. 5.7. Following the instructions. 6. Symbols and Procedures. 7. Ring Stars. 7.1. Star 4, Square from Silver Rectangle* *7.2. Star 6, Square from Silver Rectangle * * 7.3. Star 7, Square from Silver Rectangle* * 7.4. Star 5, 3 by 4 from Square ** ** 7.5. Star 5, 5 by 6 from Square Blintz ** **. 7.6. Poly Diag Star 6 ** **. 7.7. Poly Diag Star 5 ** ** 7.8. Poly Diag Star 8 ** ** 7.9. Boat Unit 5 Pentagram ** ** 7.10. Boat Unit 6 Hexagram ** ** 7.11. Boat Unit 7 Heptagram ** ** 8. Wreaths. 8.1. Swirl 10, Square from Silver Rectangle* * 8.2. Octagram Wreath * * 8.3. Octagram Paper Cup - Kite Wheel ** ** 8.4. Kite Wheel 10 *** ** 8.5. Decagon Ring * * 8.6. Handshake Wreath 8 * * 8.7. Hook and Roll Wreath 8 ** ** 8.8. Star 8 Octad * * 8.9. Starburst 8 Octad * * 8.10. Starburst 8 60◦ ** 8.11. Starburst 6 * * 9. Stars. 9.1. Star 3, Square from Silver Rectangle * * 9.2. Silver Star 7 ** ** 9.3. Star 6 * * 9.4. Pentagram ** *** 9.5. Star 6, Bronze Rectangle from Square ** * 9.6. Handshake Star 6 * * 9.7. Star 4, Kite from Silver Rectangle * * 9.8. Star 5 From Half Silver Rectangle * * 9.9. Star 4 Leftover Wrap * * 9.10. Star 6 Bronze Wrap * * 9.11. Star 8 Leftover Wrap 45◦ * ** 9.12. Star 8 Leftover Wrap 22.5◦ ** ** 9.13. Medallion Star ** *** 9.14. Star 6 Fancy Wrap *** *** 9.15. Star 6, Equilateral Triangle from Rectangle * * 9.16. Star 6 Bronze Triangle Wheel ** ** 9.17. Intersecting Squares ** ** 9.18. Quilt Star ** ** 9.19. Three Four Dodecagon Squares ** ** 10. Sliders. 10.1. Star 4 Slider, Square Silver from Rectangle * * 10.2. Square Pointer Slider ** ** 10.3. Pinwheel Square Slider ** ** 10.4. Pinwheel Square 3D Slider *** ** 10.5. Octagram Slider * * 10.6. Floppy Slider 8 * * 10.7. Floppy Slider 6 * * 10.8. Slider N 8 ** ** 10.9. Slider N 6 ** ** 10.10. Slider N 5 ** ** 11. 3D Stars. 11.1. Starfish * * 11.2. XYZ Rhombic * * 11.3. Star Ball ** *** 11.4. WXYZ *** *** 11.5. Blintz Icosidodecahedron ** **** 12. Notes for Teachers 12.1. Common folding problems and how to avoid them. 12.2. General tasks. 12.3. Specific mathematical topics. 13. Further Reading. 13.1. Origami. 13.2. Mathematics and Geometry. 13.3. Origami and Mathematics. 13.4. Origami and Mathematics Education. Bibliography. Index.

Biography

Tung Ken Lam is an origami creator, author, and qualified mathematics teacher.

His best-known works are WXYZ (p. 108) and Jitterbug. He is the author of Action Modular Origami to Intrigue and Delight (Tarquin, 2018), and coauthor of Learning Mathematics with Origami (Association of Teachers of Mathematics, 2016).

He has taught and presented his origami work in France, Italy, Sweden, Japan, and USA. He has run many events for teachers, learners, and the general public. He accepts commissions for origami projects and creating bespoke origami to order. Clients have included Bletchley Park Trust, The Bodleian Library, University of Oxford, EuroStemCell (formerly the Scottish Centre for Regenerative Medicine) and Honda UK.

"Star Origami is a festival of folding fun that is sure to inspire. Ken's stellar designs are rich with invention and, as always, his works are beautifully written and illustrated. Those eager for the　math behind the designs will not be disappointed—this is one of Tung Ken Lam's most exemplary efforts and not to be missed!
— Michael LaFosse (Origamido® Studio) author of over 50 origami books including Geometric Origami: The Art of Modular Paper Sculpture

"The modular origami-star creator faces an unlimited world of design possibilities, from random fidgeting to myriad explorations guided by mathematics.　 For the latter, Star Origami provides a treasure trove of relevant math foundations, and suggestive pathways for the creative journey. It has already stimulated new directions for my own star structures."
– Arnold Tubis, Author of Unfolding Mathematics with Origami Boxes and Tessellation Inspired Origami Box Designs

"Tung Ken Lam is one of the world’s leading exponents of modular origami design. His books never disappoint."
– David Mitchell, author of Mathematical Origami and founder of www.origamiheaven.com

"A handy catalog of classes of rectangles and their mathematical properties. Perfect for teachers who can guide students in an exploration of the relationship between the properties of rectangles and stars that can be formed from them by folding. The curious and motivated student will find hours of mathematical buried treasure through folding."
– Charlene Morrow, Director, SummerMath, Mount Holyoke College and Pas Board Chair, OrigamiUSA

"[T]he combination of artistic creativity and mathematical precision is both astounding and inspirational in equal measures."
– Sep Riahi, CEO, Global Tinker

"A beautifully written and easy to navigate guide to folding a wonderful range of modular origami stars, from simple models suitable for children and beginners, to more complex models to challenge and delight the experienced folder.

This is a wonderful compendium for teachers of mathematics, containing many simple but pleasing models suitable for children and beginners, several of which can be made from A4 printer paper, perfect for the busy teacher! Tung Ken Lam also includes a comprehensive section to support teachers to manage the activities in a classroom, showing how to gently draw out the mathematics inherent in the paper folding process. There are also instructions for exploring the designs in computer graphics and dynamic geometry programs.

Truly a treasure of a book!"
– Clarissa Grandi, author of the Artful Maths books and ArtfulMaths.com.

"Profusely and effectively illustrated step-by-step instructions, Star Origami: The Starrygami Galaxy of Modular Origami Stars, Rings and Wreaths is an ideal introduction to the mathematics of creating origami stars"
– Midwest Books Review

"In every book, we look for something unique, something that draws our attention or gives us some added value beyond only the models. This book is surprising in a few aspects. First, the extra material around the models is huge. The author even went far and wrote code lines for Turtle-Graphic on a PC so the reader can create the polygons he is talking about. The first 40 pages have many gems and a lot of relevant knowledge to help the casual folder learn the deeper secrets of model creation or the students in a class to learn the mathematical features hidden in a sheet of paper. I must recommend the “Note for Teachers” chapter. It is highly useful for making sure the class will succeed in folding the models and learning relevant aspects from the geometric domain.

Bottom line: Highly recommended for teachers and for folders who want more than a few more models!"
– Ilan Garibi, The Fold, OrigamiUSA