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1 results

  • 7 - Counting Flat Folds

  • 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 137-158

  • Summary

    Chapter 7 delves into a handful of combinatorial problems in flat origami theory that are more general than the single-vertex problems considered in Chapter 5. First, we count the number of locally-valid mountain-valley assignments of certain origami tessellations, like the square twist and Miura-ori tessellations. Then the stamp-folding problem is discussed, where the crease pattern is a grid of squares and we want to fold them into a one-stamp pile in as many ways as possible.Then the tethered membrane model of polymer folding is considered from soft-matter physics, which translates into origami as counting the number of flat-foldable crease patterns that can be made as a subset of edges from the regular triangle lattice.Many of these problems establish connections between flat foldings and graph colorings and statistical mechanics.