An Efficient Triangulation of $\mathbb{R}P^5$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918379576623104 |
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| author | Guyer, Dan Steinerberger, Stefan Yang, Yirong |
| author_facet | Guyer, Dan Steinerberger, Stefan Yang, Yirong |
| contents | We present a $6$-dimensional centrally symmetric simplicial polytope for which the antipodal quotient of its boundary forms a $24$-vertex triangulation of the $5$-dimensional real projective space. This $6$-polytope is highly symmetric with an automorphism group of order $192$, and is of independent interest. We conjecture that our construction uses the fewest number of vertices among all triangulations of $\mathbb{R}P^5$. Our method also produces two triangulations of $\mathbb{R}P^6$ on $45$ and $49$ vertices; both improve the previously best known construction in dimension $6$ that used $53$ vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Efficient Triangulation of $\mathbb{R}P^5$ Guyer, Dan Steinerberger, Stefan Yang, Yirong Combinatorics Geometric Topology 57Q15, 52B12 We present a $6$-dimensional centrally symmetric simplicial polytope for which the antipodal quotient of its boundary forms a $24$-vertex triangulation of the $5$-dimensional real projective space. This $6$-polytope is highly symmetric with an automorphism group of order $192$, and is of independent interest. We conjecture that our construction uses the fewest number of vertices among all triangulations of $\mathbb{R}P^5$. Our method also produces two triangulations of $\mathbb{R}P^6$ on $45$ and $49$ vertices; both improve the previously best known construction in dimension $6$ that used $53$ vertices. |
| title | An Efficient Triangulation of $\mathbb{R}P^5$ |
| topic | Combinatorics Geometric Topology 57Q15, 52B12 |
| url | https://arxiv.org/abs/2603.07808 |