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- W2997473813 abstract "Abstract We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flexion of a Kokotsakis polyhedron must be reducible. Izmestiev [3] showed that a polyhedron of the orthodiagonal anti-involutive type is the only possible candidate to disprove Stachel’s conjecture. We show that the corresponding resultant is reducible, thereby confirming the conjecture. We do it in two ways: by factorization of the corresponding resultant and providing a simple geometric proof. We describe the space of parameters for which such a polyhedron exists and show that this space is non-empty. We show that a Kokotsakis polyhedron of orthodiagonal anti-involutive type is flexible and give explicit parametrizations in elementary functions and in elliptic functions of its flexion." @default.
- W2997473813 created "2020-01-10" @default.
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- W2997473813 date "2020-04-01" @default.
- W2997473813 modified "2023-09-24" @default.
- W2997473813 title "Orthodiagonal anti-involutive Kokotsakis polyhedra" @default.
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- W2997473813 doi "https://doi.org/10.1016/j.mechmachtheory.2019.103713" @default.
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