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arXiv · 1607.06604

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

Victor Alexandrov
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Abstract

We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric to $P$, and $\textrm{vol} Q>c\cdot \textrm{vol} P>0$.

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Victor Alexandrov. 2017-03-01. How many times can the volume of a convex polyhedron be increased by isometric deformations?. https://doi.org/10.1007/s13366-017-0336-8

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