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1 results

  • 5 - Flat Vertex Folds: Local Properties

  • from Part II - The Combinatorial Geometry of Flat Origami
  • Thomas C. Hull
  • Book:
    Origametry
    Published online:
    06 October 2020
    Print publication:
    08 October 2020, pp 75-106

  • 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.