2015/07/06 by Zachary Abel, Jason Cantarella, Erik D. Demaine +5 · 21 citations
Computer Science · Engineering · Mathematics · #Advanced Materials and Mechanics #Combinatorics #Computational Geometry and Mesh Generation #Computer science #Forcing (mathematics) #Graph #Mathematical analysis #Mathematics #Vertex (graph theory) #math.CO #math.MG #msc:52C25 #msc:74P10
paper · pdf · doi:10.20382/jocg.v7i1a9
published in Journal of Computational Geometry (Carleton University) (Carleton University)
arxiv created 2015/07/06 · openalex publication_date 2015/11/25 · arxiv updated 2016/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.