%0 Generic %1 hull2013combinatorics %A Hull, Thomas C. %D 2013 %K origami %T The Combinatorics of Flat Folds: a Survey %U http://arxiv.org/abs/1307.1065 %X 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.

@misc{hull2013combinatorics, 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.}, added-at = {2014-12-08T23:05:45.000+0100}, author = {Hull, Thomas C.}, biburl = {https://www.bibsonomy.org/bibtex/20f82b40bb8e34bd236c949982b706371/wolftype}, description = {[1307.1065] The Combinatorics of Flat Folds: a Survey}, interhash = {6a95707ef03d65fd06d3230f885399fc}, intrahash = {0f82b40bb8e34bd236c949982b706371}, keywords = {origami}, note = {cite arxiv:1307.1065Comment: 10 pages, 4 figures}, timestamp = {2014-12-08T23:05:45.000+0100}, title = {The Combinatorics of Flat Folds: a Survey}, url = {http://arxiv.org/abs/1307.1065}, year = 2013 }