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arxiv: 1605.09316 · v1 · pith:UPPVFDBUnew · submitted 2016-05-30 · 🧮 math.MG · math.AG

Flexible Polyhedra and Their Volumes

Alexander A. Gaifullin This is my paper
classification 🧮 math.MG math.AG
keywords flexiblepolyhedraareabellowsclaimsconjectureconstantdiscuss
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We discuss some recent results on flexible polyhedra and the bellows conjecture, which claims that the volume of any flexible polyhedron is constant during the flexion. Also, we survey main methods and several open problems in this area.

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  1. Exotic spherical flexible octahedra and counterexamples to the Modified Bellows Conjecture

    math.MG 2025-03 unverdicted novelty 6.0

    Exotic spherical flexible octahedra have non-constant volume under flexion and after antipodal replacements, providing counterexamples to the Modified Bellows Conjecture.