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  1. README.md +53 -0
  2. polytopes-4d-05-vertices.parquet +3 -0
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README.md ADDED
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+ ---
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+ license: cc-by-sa-4.0
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+ pretty_name: Four-Dimensional Reflexive Lattice Polytopes
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+ configs:
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+ - config_name: default
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+ data_files:
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+ - split: full
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+ path: "*.parquet"
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+ size_categories:
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+ - 100K<n<1M
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+ tags:
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+ - physics
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+ - math
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+ ---
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+
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+ # Four-Dimensional Reflexive Lattice Polytopes
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+
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+ This dataset contains all four-dimensional reflexive lattice polytopes. The data was
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+ compiled by Maximilian Kreuzer and Harald Skarke in
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+ [arXiv:hep-th/0002240](https://arxiv.org/abs/hep-th/0002240).
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+
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+ Please cite the paper when referencing this dataset:
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+
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+ ```
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+ @article{Kreuzer:2000xy,
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+ author = "Kreuzer, Maximilian and Skarke, Harald",
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+ title = "{Complete classification of reflexive polyhedra in four-dimensions}",
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+ eprint = "hep-th/0002240",
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+ archivePrefix = "arXiv",
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+ reportNumber = "HUB-EP-00-13, TUW-00-07",
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+ doi = "10.4310/ATMP.2000.v4.n6.a2",
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+ journal = "Adv. Theor. Math. Phys.",
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+ volume = "4",
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+ pages = "1209--1230",
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+ year = "2000"
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+ }
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+ ```
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+
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+ ## Dataset Details
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+
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+ This dataset is licensed under the
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+ [CC BY-SA 4.0 license](http://creativecommons.org/licenses/by-sa/4.0/).
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+
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+ ### Data Fields
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+
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+ - `vertices`: Vertex positions of the polytope in normalized form.
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+ - `vertex_count`: Vertex count of the polytope.
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+ - `facet_count`: Facet count of the polytope.
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+ - `point_count`: Lattice point count of the polytope.
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+ - `dual_point_count`: Lattice point count of the dual polytope.
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+ - `h11`: Hodge number \\( h^{1,1} \\).
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+ - `h12`: Hodge number \\( h^{1,2} \\).
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+ - `euler_characteristic`: Euler characteristic of the polytope.
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