Abstract
A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, to a flat position, in such a way that the paper is not torn, stretched and, for rigid origami, not bent anywhere except along the given creases.Streinu and Whiteley showed how to reduce the single-vertex origami problem to the Carpenter's Rule Problem for spherical polygons. Using spherical expansive motions, they solved the cases of open
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