Corpus ID: 221995541

Zero-sum cycles in flexible polyhedra

  title={Zero-sum cycles in flexible polyhedra},
  author={Matteo Gallet and Georg Grasegger and Jan Legersk'y and J. Schicho},
  journal={arXiv: Metric Geometry},
We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously deformed preserving the shape of its faces, then there is a cycle of edges whose lengths sum up to zero once suitably weighted by 1 and -1. We do this via elementary combinatorial considerations, made possible by a well-known compactification of the three-dimensional affine space as a quadric in the four-dimensional projective space. The compactification is related to… Expand
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