---
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.