Vertices on Quasigeodesics

Joseph O’Rourke () and Costin Vîlcu ()
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Joseph O’Rourke: Smith College
Costin Vîlcu: Romanian Academy

Chapter Chapter 17 in Reshaping Convex Polyhedra, 2024, pp 213-219 from Springer

Abstract: 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.

Date: 2024
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DOI: 10.1007/978-3-031-47511-5_17

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