Counterexamples to the Modified Bellows Conjecture from exotic flexible cross-polytopes

Let $n\ge 4$, and consider exotic flexible cross-polytopes in the sphere $\mathbb{S}^n$. These are flexible cross-polytopes whose dihedral-angle tangents have the exotic parametrizations described in the source. Counterexample claim. Exotic flexible cross-polytopes provide counterexamples to the Modified Bellows Conjecture in $\mathbb{S}^n$ for all $n\ge 4$. This claim gives the higher-dimensional counterexamples that refute the Modified Bellows Conjecture. The source explains that no geometric construction of these higher-dimensional exotic flexible cross-polytopes is known, and that proving the claim may require cumbersome calculations with elliptic functions.