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arXiv · 1307.1065

The Combinatorics of Flat Folds: a Survey

Thomas C. Hull
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Abstract

We survey results on the foldability of flat origami models. The main topics are the question of when a given crease pattern can fold flat, the combinatorics of mountain and valley creases, and counting how many ways a given crease pattern can be folded. In particular, we explore generalizations of Maekawa's and Kawasaki's Theorems, develop a necessary and sufficient condition for a given assignment of mountains and valleys to fold up in a special case of single vertex folds, and describe recursive formulas to enumerate the number of ways that single vertex in a crease pattern can be folded.

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Thomas C. Hull. 2013-07-03. The Combinatorics of Flat Folds: a Survey. https://arxiv.org/abs/1307.1065

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