aschachner/KS_Cornell
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--- pretty_name: KS database for string theory size_categories: - 100M<n<1B license: cc-by-sa-4.0 --- This dataset is based on the [Kreuzer–Skarke database](http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYcy.html), which classifies all 473,800,776 reflexive lattice polytopes in four dimensions as enumerated by Maximilian Kreuzer and Harald Skarke. It contains additional geometric and combinatorial information about these polytopes that is particularly relevant for string theory compactifications and model building. The dataset was primarily developed to interface with [CYTools](https://cy.tools), a software package for the analysis of Calabi–Yau hypersurfaces in toric varieties, created by the group of Prof. Liam McAllister at Cornell University. For questions, please contact [as3475@cornell.edu](mailto:as3475@cornell.edu) or the developers of [CYTools](https://cy.tools). ## Dataset Details This dataset is licensed under the [CC BY-SA 4.0 license](http://creativecommons.org/licenses/by-sa/4.0/). ### Data Fields - `h11`: The Hodge number h^{1,1} of the associated Calabi–Yau threefold hypersurface. - `h12`: The Hodge number h^{2,1} of the associated Calabi–Yau threefold hypersurface. - `ks_id`: Identifier of the polytope corresponding to the ordering for fixed \( h^{1,1} \) in the original Kreuzer–Skarke database. - `fav_N`: Boolean flag indicating whether the polytope is favourable in the \(N\)-lattice. - `fav_M`: Boolean flag indicating whether the dual polytope is favourable in the \(M\)-lattice. - `trilayer`: Boolean flag indicating whether the polytope is trilayer. - `n_rigids`: #rigid prime toric divisors associated with the polytope. - `n_1faces`: #1-dimensional faces (1-faces, edges) of the polytope. - `n_2faces`: #2-dimensional faces (2-faces) of the polytope. - `n_3faces`: #3-dimensional faces (3-faces, facets) of the polytope. - `max_2face`: Maximum number of lattice points contained in any 2-dimensional face. - `vertices`: List of lattice vertices defining the four-dimensional reflexive polytope. - `n_pts_1faces`: #points of each 1-face. - `n_int_pts_1faces`: #interior points in each 1-face. - `n_pts_2faces`: #points of each 2-face. - `n_int_pts_2faces`: #interior points in each 2-face. - `n_pts_3faces`: #points of each 3-face. - `n_int_pts_3faces`: #interior points in each 3-face. - `n_int_pts_dual_1faces`: #interior points in each dual 1-face. - `n_int_pts_dual_2faces`: #interior points in each dual 2-face. - `n_int_pts_dual_3faces`: #interior points in each dual 3-face.
展示名称：弦理论KS数据库 规模类别：100M<n<1B 许可协议：CC BY-SA 4.0 本数据集基于[Kreuzer–Skarke数据库（Kreuzer–Skarke database）](http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYcy.html)，该数据库由马克西米利安·克罗伊策（Maximilian Kreuzer）与哈拉尔德·斯卡克（Harald Skarke）完成枚举，分类了四维空间中总计473,800,776个自反格多胞体（reflexive lattice polytopes）。数据集额外收录了这些多胞体的几何与组合学信息，此类信息对弦理论紧化研究与模型构建具有关键价值。 本数据集的开发主要为适配[CYTools](https://cy.tools)，CYTools是康奈尔大学利亚姆·麦卡利斯特（Liam McAllister）教授团队研发的软件包，用于分析托里克斯簇（toric varieties）中的卡拉比-丘超曲面（Calabi–Yau hypersurface）。 如有疑问，请联系[as3475@cornell.edu]或CYTools的开发者。 ## 数据集详情 本数据集采用[CC BY-SA 4.0许可协议](http://creativecommons.org/licenses/by-sa/4.0/)授权。 ### 数据字段 - `h11`：对应关联卡拉比-丘三维超曲面的霍奇数（Hodge number）$h^{1,1}$ - `h12`：对应关联卡拉比-丘三维超曲面的霍奇数$h^{2,1}$ - `ks_id`：原始Kreuzer–Skarke数据库中，针对固定$h^{1,1}$的排序规则下，该多胞体的标识符 - `fav_N`：布尔标记，用于指示该多胞体在$N$格中是否为优型多胞体 - `fav_M`：布尔标记，用于指示该多胞体的对偶多胞体在$M$格中是否为优型多胞体 - `trilayer`：布尔标记，用于指示该多胞体是否为三层结构多胞体 - `n_rigids`：与该多胞体相关的刚性素托里克斯除子的数量 - `n_1faces`：该多胞体的1维面（1-面，即棱）的数量 - `n_2faces`：该多胞体的2维面的数量 - `n_3faces`：该多胞体的3维面（3-面，即胞）的数量 - `max_2face`：任意单条2维面所包含的格点的最大数量 - `vertices`：定义该四维自反格多胞体的格顶点列表 - `n_pts_1faces`：每个1维面所包含的格点总数 - `n_int_pts_1faces`：每个1维面内部所包含的格点总数 - `n_pts_2faces`：每个2维面所包含的格点总数 - `n_int_pts_2faces`：每个2维面内部所包含的格点总数 - `n_pts_3faces`：每个3维面所包含的格点总数 - `n_int_pts_3faces`：每个3维面内部所包含的格点总数 - `n_int_pts_dual_1faces`：每个对偶1维面内部所包含的格点总数 - `n_int_pts_dual_2faces`：每个对偶2维面内部所包含的格点总数 - `n_int_pts_dual_3faces`：每个对偶3维面内部所包含的格点总数
