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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18308 |
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| _version_ | 1866911329139294208 |
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| author | Chen, Hao Markande, Shashank G. Saba, Matthias Schröder-Turk, Gerd E. Matsumoto, Elisabetta A. |
| author_facet | Chen, Hao Markande, Shashank G. Saba, Matthias Schröder-Turk, Gerd E. Matsumoto, Elisabetta A. |
| contents | This paper provides a construction and existence proof for a 1-parameter family of chiral unbalanced triply-periodic minimal surfaces of genus 4. We name these {\textit{gyrating H'-T} surfaces, because they are related to Schoen's H'-T surfaces in a similar way as the Gyroid is to the Primitive surface. Their chirality is manifest in a screw symmetry of order six. The two labyrinthine domains on either side of the surface are not congruent, rather one representing the quartz net (\texttt{qtz}) and the other one the dual of the quartz net (\texttt{qzd}). The family tends to the Scherk saddle tower in one limit and to the doubly periodic Scherk surface in the other. The motivation for the construction was to construct a chiral tunable unbalanced surface family, originally as a template for photonic materials. The numeric construction is based on reverse-engineering of the tubular surface of two suitably chosen dual nets, using the \textit{Surface Evolver}} to minimize area or curvature variations. The existence is proved using Weierstrass parametrizations defined on the branched torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The chiral gyrating H'-T surface family: construction from the dual qtz--qzd nets and existence proof using a toroidal Weierstrass method Chen, Hao Markande, Shashank G. Saba, Matthias Schröder-Turk, Gerd E. Matsumoto, Elisabetta A. Differential Geometry Materials Science This paper provides a construction and existence proof for a 1-parameter family of chiral unbalanced triply-periodic minimal surfaces of genus 4. We name these {\textit{gyrating H'-T} surfaces, because they are related to Schoen's H'-T surfaces in a similar way as the Gyroid is to the Primitive surface. Their chirality is manifest in a screw symmetry of order six. The two labyrinthine domains on either side of the surface are not congruent, rather one representing the quartz net (\texttt{qtz}) and the other one the dual of the quartz net (\texttt{qzd}). The family tends to the Scherk saddle tower in one limit and to the doubly periodic Scherk surface in the other. The motivation for the construction was to construct a chiral tunable unbalanced surface family, originally as a template for photonic materials. The numeric construction is based on reverse-engineering of the tubular surface of two suitably chosen dual nets, using the \textit{Surface Evolver}} to minimize area or curvature variations. The existence is proved using Weierstrass parametrizations defined on the branched torus. |
| title | The chiral gyrating H'-T surface family: construction from the dual qtz--qzd nets and existence proof using a toroidal Weierstrass method |
| topic | Differential Geometry Materials Science |
| url | https://arxiv.org/abs/2512.18308 |