Vertex-minimal hyperbolic origami 2-torus
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908660094992384 |
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| author | Zou, Zhengyu |
| author_facet | Zou, Zhengyu |
| contents | We show that there exists a geodesic triangulation $T$ of a hyperbolic genus 2 surface $Σ_2$ with 10 vertices and an isometric polyhedral embedding $S: Σ_2 \hookrightarrow \mathbb{H}^3$ that sends the triangles in $T$ to geodesic triangles in $\mathbb{H}^3$. We call this type of embedding a hyperbolic origami 2-torus. Since 10 is the combinatorially minimum number of vertices required to triangulate a genus 2 surface, this paper settles the question of minimum number of vertices required to obtain a hyperbolic origami 2-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vertex-minimal hyperbolic origami 2-torus Zou, Zhengyu Metric Geometry Geometric Topology 52B70, 57Q35 (Primary), 51M10, 57Q15 (Secondary) We show that there exists a geodesic triangulation $T$ of a hyperbolic genus 2 surface $Σ_2$ with 10 vertices and an isometric polyhedral embedding $S: Σ_2 \hookrightarrow \mathbb{H}^3$ that sends the triangles in $T$ to geodesic triangles in $\mathbb{H}^3$. We call this type of embedding a hyperbolic origami 2-torus. Since 10 is the combinatorially minimum number of vertices required to triangulate a genus 2 surface, this paper settles the question of minimum number of vertices required to obtain a hyperbolic origami 2-torus. |
| title | Vertex-minimal hyperbolic origami 2-torus |
| topic | Metric Geometry Geometric Topology 52B70, 57Q35 (Primary), 51M10, 57Q15 (Secondary) |
| url | https://arxiv.org/abs/2509.18668 |