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Vertices on Quasigeodesics

In: Reshaping Convex Polyhedra

Author

Listed:
  • Joseph O’Rourke

    (Smith College)

  • Costin Vîlcu

    (Romanian Academy)

Abstract

Theorem 16.5 demonstrated the importance in our context of the number of vertices on a quasigeodesic.quasigeodesicnumber of vertices If, as we conjecture in Open Problem 18.15 , every convex polyhedron P has a quasigeodesic Q $$\mathcal {Q}$$ containing at most one vertex, then the vertex-mergingvertex-merging described in that theorem leads to an unfoldingunfoldingonto cylinder of P to a cylinder ℒ $$\mathcal {L}$$ and then to a non-overlapping unfolding, an anycut-netnetanycut- for P.

Suggested Citation

  • Joseph O’Rourke & Costin Vîlcu, 2024. "Vertices on Quasigeodesics," Springer Books, in: Reshaping Convex Polyhedra, chapter 0, pages 213-219, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-47511-5_17
    DOI: 10.1007/978-3-031-47511-5_17
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