The Combinatorics of Flat Folds: a Survey
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.1065
- arXiv:
- arXiv:1307.1065
- Bibcode:
- 2013arXiv1307.1065H
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Combinatorics;
- 05A02
- E-Print:
- 10 pages, 4 figures