Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- Part I Geometric Constructions
- Part II The Combinatorial Geometry of Flat Origami
- 5 Flat Vertex Folds: Local Properties
- 6 Multiple-Vertex Flat Folds: Global Properties
- 7 Counting Flat Folds
- 8 Other Flat-Folding Problems
- Part III Algebra, Topology, and Analysis in Origami
- Part IV Non-flat Folding
- References
- Index
5 - Flat Vertex Folds: Local Properties
from Part II - The Combinatorial Geometry of Flat Origami
Published online by Cambridge University Press: 06 October 2020
- Frontmatter
- Dedication
- Contents
- Introduction
- Part I Geometric Constructions
- Part II The Combinatorial Geometry of Flat Origami
- 5 Flat Vertex Folds: Local Properties
- 6 Multiple-Vertex Flat Folds: Global Properties
- 7 Counting Flat Folds
- 8 Other Flat-Folding Problems
- Part III Algebra, Topology, and Analysis in Origami
- Part IV Non-flat Folding
- References
- Index
Summary
The field of flat-foldable origami is introduced, which involves a mix of geometry and combinantorics.This chapter focuses on local properties of flat origami, meaning the study of how and when a single vertex in an origami crease pattern will be able to fold flat.The classic theorems of Kawasaki and Maekawa are proved and generalizations are made to folding vertices on cone-shaped (i.e., non-developable) paper.The problem of counting valid mountain-valley assignments of flat-foldable vertices is solved, and the configuration space of flat-foldable vertices of a fixed degree is characterized.A matrix model for formalizing flat-vertex folds is introduced, and the chapter ends with historical notes on this topic.
Keywords
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- Chapter
- Information
- OrigametryMathematical Methods in Paper Folding, pp. 75 - 106Publisher: Cambridge University PressPrint publication year: 2020