Unfolding Convex Polyhedra via Quasigeodesics. Jin-ichi Ito (Kumamoto Univ.) Joseph O’Rourke (Smith College) Costin V î lcu (S.-S. Romanian Acad.). General Unfoldings of Convex Polyhedra. Theorem : Every convex polyhedron has a general nonoverlapping unfolding (a net).
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Jin-ichi Ito (Kumamoto Univ.)
Joseph O’Rourke (Smith College)
Costin Vîlcu (S.-S. Romanian Acad.)
[Xu, Kineva, O’Rourke 1996, 2000]
Theorem: Every closed surface homeomorphic to a sphere has at least three, distinct closed geodesics.
at each point p of curve.
[Lysyanskaya, O’Rourke 1996]
Is there an algorithm
or efficient numerical algorithm
for finding a closed quasigeodesic on a (convex) polyhedron?