How many times can the volume of a convex polyhedron be increased by isometric deformations?

DOI10.1007/s13366-017-0336-8zbMath1387.52024arXiv1607.06604OpenAlexW2508923275MaRDI QIDQ2402912

Victor Alexandrov

Publication date: 15 September 2017

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06604

zbMATH Keywords

Euclidean spaceconvex polyhedronintrinsic metricbipyramidintrinsic isometryvolume increasing deformation

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Optimization of shapes other than minimal surfaces (49Q10) Isoperimetric problems for polytopes (52B60) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Cites Work

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• Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions
• Volume increasing isometric deformations of convex polyhedra
• Volume increasing isometric deformations of polyhedra
• Algebraic methods for solution of polyhedra
• Inflating the Cube Without Stretching

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