Star Origami

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.

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.