An Elliptic Curve Governing Hopf Linking in an $A_4$-Symmetric Tensegrity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918456719310848 |
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| author | Sadahiro, Taizo |
| author_facet | Sadahiro, Taizo |
| contents | We study in detail an A4-symmetric tensegrity appearing in Connelly's catalog. The realizable configurations form a one-parameter family that can be parametrized by points on the elliptic curve with Cremona label 30a2. The curve has only twelve rational points, among which only one corresponds to a stable tensegrity configuration whose cable framework forms a cuboctahedron. From a topological viewpoint, however, the underlying pair of the strut triangles preserves a Hopf link structure throughout the entire interval 0 < ω_1 < 1 of the stress parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Elliptic Curve Governing Hopf Linking in an $A_4$-Symmetric Tensegrity Sadahiro, Taizo Geometric Topology We study in detail an A4-symmetric tensegrity appearing in Connelly's catalog. The realizable configurations form a one-parameter family that can be parametrized by points on the elliptic curve with Cremona label 30a2. The curve has only twelve rational points, among which only one corresponds to a stable tensegrity configuration whose cable framework forms a cuboctahedron. From a topological viewpoint, however, the underlying pair of the strut triangles preserves a Hopf link structure throughout the entire interval 0 < ω_1 < 1 of the stress parameter. |
| title | An Elliptic Curve Governing Hopf Linking in an $A_4$-Symmetric Tensegrity |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2604.18116 |