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Abstract: In the study of flat origami, each crease pattern has an associated set of valid mountain-valley assignments - ones that will allow it to fold flat. We study how these assignments for single-vertex crease patterns are related to one another through face flips, where flipping a face means switching the assignment of all bordering creases. Specifically, we explore the origami flip graph OFG(C) of a given crease pattern C where each vertex is a valid mountain-valley assignment for C and two vertices are adjacent if their assignments differ by a single face flip. We show how different origami flip graphs of single-vertex crease patterns are related and provide an edge count for the maximal case. Joint work with Thomas C. Hull, Manuel Morales, and Sarah Nash

Zoom link: https://rutgers.zoom.us/j/94346444480
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