Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- Part I Geometric Constructions
- Part II The Combinatorial Geometry of Flat Origami
- Part III Algebra, Topology, and Analysis in Origami
- 9 Origami Homomorphisms
- 10 Folding Manifolds
- 11 An Analytic Approach to Isometric Foldings
- Part IV Non-flat Folding
- References
- Index
9 - Origami Homomorphisms
from Part III - Algebra, Topology, and Analysis in Origami
Published online by Cambridge University Press: 06 October 2020
Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- Part I Geometric Constructions
- Part II The Combinatorial Geometry of Flat Origami
- Part III Algebra, Topology, and Analysis in Origami
- 9 Origami Homomorphisms
- 10 Folding Manifolds
- 11 An Analytic Approach to Isometric Foldings
- Part IV Non-flat Folding
- References
- Index
Summary
In Chapter 9 we explore the work of Kawasaki and Yoshida from1988, where group theory is used to relate the symmetries of a flat origami crease pattern to the symmetries of its folded image.This is then applied to origami tessellations to show that if the tessellation’s symmetries form a crystallographic group of the plane, then the symmetry group of the folded paper must be isomorphic to the symmetry group of the crease pattern.
Keywords
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- Chapter
- Information
- OrigametryMathematical Methods in Paper Folding, pp. 181 - 190Publisher: Cambridge University PressPrint publication year: 2020