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

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 $\text{vol}Q>c\cdot \text{vol}P>0$.

5 pages, 2 figures. In version 2, several formulas are corrected

References in corpus (1)

• Generalization of Sabitov's Theorem to Polyhedra of Arbitrary Dimensions