---
license: cc-by-sa-4.0
pretty_name: Four-Dimensional Reflexive Lattice Polytopes
configs:
  - config_name: default
    data_files:
      - split: full
        path: "*.parquet"
size_categories:
  - 100M<n<1B
tags:
  - physics
  - math
---

# Four-Dimensional Reflexive Lattice Polytopes

This dataset contains all four-dimensional reflexive lattice polytopes. The data was
compiled by Maximilian Kreuzer and Harald Skarke in
[arXiv:hep-th/0002240](https://arxiv.org/abs/hep-th/0002240). More information is
available at the [Calabi-Yau data website](http://hep.itp.tuwien.ac.at/~kreuzer/CY/).

Please cite the paper when referencing this dataset:

```
@article{Kreuzer:2000xy,
    author = "Kreuzer, Maximilian and Skarke, Harald",
    title = "{Complete classification of reflexive polyhedra in four-dimensions}",
    eprint = "hep-th/0002240",
    archivePrefix = "arXiv",
    reportNumber = "HUB-EP-00-13, TUW-00-07",
    doi = "10.4310/ATMP.2000.v4.n6.a2",
    journal = "Adv. Theor. Math. Phys.",
    volume = "4",
    pages = "1209--1230",
    year = "2000"
}
```

## Dataset Details

This dataset is licensed under the
[CC BY-SA 4.0 license](http://creativecommons.org/licenses/by-sa/4.0/).

### Data Fields

- `vertices`: Vertex positions of the polytope in normal form.
- `vertex_count`: Vertex count of the polytope.
- `facet_count`: Facet count of the polytope.
- `point_count`: Lattice point count of the polytope.
- `dual_point_count`: Lattice point count of the dual polytope.
- `h11`: Hodge number \\( h^{1,1} \\).
- `h12`: Hodge number \\( h^{1,2} \\).
- `euler_characteristic`: Euler characteristic of the polytope.