Hamiltonian Quasigeodesics yield Nets
Joseph O'Rourke
TL;DR
This paper proves that polyhedra with Hamiltonian quasigeodesics can be unfolded into nets, expanding the class of polyhedra known to have such unfoldings and demonstrating that this class is infinite.
Contribution
It introduces the concept that polyhedra with Hamiltonian quasigeodesics can always be edge-unfolded into nets, showing this class is infinite.
Findings
Polyhedra with Hamiltonian quasigeodesics can be edge-unfolded into nets.
The class of polyhedra with Hamiltonian quasigeodesics is infinite.
Abstract
This note establishes that every polyhedron that has a Hamiltonian quasigeodesic can be edge-unfolded to a net, and shows that the class of such polyhedra is infinite.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Advanced Numerical Analysis Techniques