Uniquely realizable crystalline structures
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911226920960000 |
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| author | Dewar, Sean Schulze, Bernd Tanigawa, Shin-ichi Theran, Louis |
| author_facet | Dewar, Sean Schulze, Bernd Tanigawa, Shin-ichi Theran, Louis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniquely realizable crystalline structures Dewar, Sean Schulze, Bernd Tanigawa, Shin-ichi Theran, Louis Metric Geometry Algebraic Geometry Combinatorics 52C25 (Primary) 05C62, 14P99 (Secondary) 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. |
| title | Uniquely realizable crystalline structures |
| topic | Metric Geometry Algebraic Geometry Combinatorics 52C25 (Primary) 05C62, 14P99 (Secondary) |
| url | https://arxiv.org/abs/2510.19529 |