Exotic spherical flexible octahedra have non-constant volume under flexion and after antipodal replacements, providing counterexamples to the Modified Bellows Conjecture.
Flexible Polyhedra and Their Volumes
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abstract
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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math.MG 1years
2025 1verdicts
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Exotic spherical flexible octahedra and counterexamples to the Modified Bellows Conjecture
Exotic spherical flexible octahedra have non-constant volume under flexion and after antipodal replacements, providing counterexamples to the Modified Bellows Conjecture.