The Combinatorics of Flat Folds: a Survey

By Thomas C. Hull. 2013

54 citations recorded by the source corpus.

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.

Subfields: Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/d79e39674e9a02d3753084d0fff3e4aad6c1fad2

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In Mechanical Engineering

1. Mihir Sen
2. Bill Goodwine
3. N. Turner

Citations in the corpus

• A review of origami applications in mechanical engineering (2016, background): “Further generalizations of these theories have been made with the intent of imposing sufficiency and investigating global foldability.(10)”