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1 results

  • 6 - Multiple-Vertex Flat Folds: Global 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 107-136

  • Summary

    Chapter 6 covers global flat foldability.This includes determining how we can tell if a crease pattern with multiple vertices will fold flat without forcing the paper to self-intersect, as well as discovering properties that all such crease patterns have, beyond what was covered in the previous chapter.Justin’s Theorem, which is a generalization of Kawasaki’s and Maekawa’s Theorems and whose proof uses elements of basic knot theory, is covered, as are Justin’s non-crossing conditions that provide necessary and sufficient conditions for a general crease pattern to fold flat.The matrix model from Chapter 5 is developed further to create a formal folding map for flat origami.Finally, Bern and Hayes’ seminal proof that determining flat foldability of a given crease pattern is NP-Hard is presented and updated with more recent results on box pleating.