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  1. ; ; ; ; ; ; (, Proc. of the 34th Canadian Conference on Computational Geometry (CCCG 2022))
    Bahoo, Y.; Georgiou, K. (Ed.)
    We introduce a notion we call quasi-twisting that cuts a convex polyhedron P into two halves and reglues the halves to form a different convex polyhedron. The cut is along a simple closed quasigeodesic. We initiate the study of the range of polyhedra produced by quasi-twisting P, and in particular, whether P can “quasi-twist flat,” i.e., produce a flat, doubly-covered polygon. We establish a sufficient condition and some necessary conditions, which allow us to show that of the five Platonic solids, the tetrahedron, cube, and oc- tahedron can quasi-twist flat. We conjecture that the dodecahedron and icosahedron cannot quasi-twist flat, and prove that they cannot under certain restrictions. Many open problems remain. 
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