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---
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.
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