Corpus ID: 235755266

Reshaping Convex Polyhedra

@article{ORourke2021ReshapingCP,
  title={Reshaping Convex Polyhedra},
  author={J. O'Rourke and Costin V{\^i}lcu},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.03153}
}
Given a convex polyhedral surface P, we define a tailoring as excising from P a simple polygonal domain that contains one vertex v, and whose boundary can be sutured closed to a new convex polyhedron via Alexandrov's Gluing Theorem. In particular, a digon-tailoring cuts off from P a digon containing v, a subset of P bounded by two equal-length geodesic segments that share endpoints, and can then zip closed. In the first part of this monograph, we primarily study properties of the tailoring… Expand