Realization and Connectivity of the Graphs of Origami Flat Foldings

17 Aug 2018  ·  Eppstein David ·

We investigate the graphs formed from the vertices and creases of an origami pattern that can be folded flat along all of its creases. As we show, this is possible for a tree if and only if the internal vertices of the tree all have even degree greater than two... However, we prove that (for unbounded sheets of paper, with a vertex at infinity representing a shared endpoint of all creased rays) the graph of a folding pattern must be 2-vertex-connected and 4-edge-connected. read more

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Computational Geometry


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