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arXiv · 2510.19529

Uniquely realizable crystalline structures

Sean Dewar·Bernd Schulze·Shin-ichi Tanigawa·Louis Theran
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Abstract

We construct infinite periodic versions of the stress matrix and establish sufficient conditions for periodic tensegrity frameworks to be globally rigid in $\mathbb{R}^d$ in the cases when the lattice is either fixed, fully flexible, or flexible with a volume constraint for the fundamental domain. For the fixed and fully flexible lattice variants, we also establish necessary and sufficient conditions for generic infinite periodic bar-joint frameworks to be globally rigid in $\mathbb{R}^d$. These results provide periodic versions of the fundamental results of Connelly, as well as Gortler, Healy and Thurston on the global rigidity of generic finite bar-joint frameworks.

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Sean Dewar, Bernd Schulze, Shin-ichi Tanigawa, Louis Theran. 2025-10-22. Uniquely realizable crystalline structures. https://arxiv.org/abs/2510.19529

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