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README.md

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+---
+license: cc-by-sa-4.0
+pretty_name: Weight Systems Defining Five-Dimensional Reflexive and Non-Reflexive Polyhedra
+configs:
+- config_name: non-reflexive
+  data_files:
+  - split: full
+    path:  non-reflexive/*.parquet
+- config_name: reflexive
+  data_files:
+  - split: full
+    path: reflexive/*.parquet
+---
+
+# Dataset of Weight Systems Defining Five-Dimensional Reflexive and Non-Reflexive Polyhedra
+
+This dataset contains all weight systems defining five-dimensional reflexive and
+non-reflexive polyhedra, instrumental in the study of Calabi-Yau fourfolds in mathematics
+and theoretical physics. The data was compiled by Friedrich Schöller and Harald Skarke in
+[arXiv:1808.02422](https://arxiv.org/abs/1808.02422). More information is available at the
+[Calabi-Yau data website](http://hep.itp.tuwien.ac.at/~kreuzer/CY/). The dataset can be
+explored using the [search frontend](http://rgc.itp.tuwien.ac.at/fourfolds/).
+
+## Dataset Details
+
+The dataset consists of two subsets: weight systems defining reflexive polyhedra and
+weight systems defining non-reflexive polyhedra. Each subset is split into 4000 files in
+Parquet format. Rows within each file are sorted lexicographically by weights.
+
+Each row in the dataset represents a polyhedron and contains the six weights defining it,
+along with the vertex count, facet count, and lattice point count. The reflexive dataset
+also includes the Hodge numbers \\( h^{1,1} \\), \\( h^{1,2} \\), and \\( h^{1,3} \\) of
+the corresponding Calabi-Yau manifold, and the lattice point count of the dual polyhedron.
+
+For any Calabi-Yau fourfold, the Euler characteristic \\( \chi \\) and the Hodge number
+\\( h^{2,2} \\) can be derived as follows:
+$$ \chi = 48 + 6 (h^{1,1} − h^{1,2} + h^{1,3}) $$
+$$ h^{2,2} = 44 + 4 h^{1,1} − 2 h^{1,2} + 4 h^{1,3} $$
+
+This dataset is licensed under the [CC BY-SA 4.0 license](http://creativecommons.org/licenses/by-sa/4.0/).
+
+### Data Fields
+
+- `weight0 to weight5:` Weights of the weight system defining the polyhedron.
+- `vertex_count:` Vertex count of the polyhedron.
+- `facet_count:` Facet count of the polyhedron.
+- `point_count:` Lattice point count of the polyhedron.
+- `dual_point_count:` Lattice point count of the dual polyhedron (only for reflexive
+  polyhedra).
+- `h11:` Hodge number \\( h^{1,1} \\) (only for reflexive polyhedra).
+- `h12:` Hodge number \\( h^{1,2} \\) (only for reflexive polyhedra).
+- `h13:` Hodge number \\( h^{1,3} \\) (only for reflexive polyhedra).
+
+## Usage
+
+The dataset can be used without downloading it entirely, thanks to the streaming
+capability of the `datasets` library. The following Python code snippet demonstrates how
+to stream the dataset and print the first five rows:
+
+```python
+from datasets import load_dataset
+
+dataset = load_dataset("cy-data/ws-5d", name="reflexive", split="full", streaming=True)
+
+for row in dataset.take(5):
+    print(row)
+```
+
+When cloning the Git repository with Git Large File Storage (LFS), data files are stored
+in the Git LFS storage directory, as well as in the working tree. To avoid occupying
+double the disk space, use a filesystem that supports copy-on-write and run the following
+commands to clone the repository:
+
+```bash
+# Initialize Git LFS
+git lfs install
+
+# Clone the repository without downloading LFS files immediately
+GIT_LFS_SKIP_SMUDGE=1 git clone https://huggingface.co/datasets/cy-data/ws-5d
+
+# Change to the repository directory
+cd ws-5d
+
+# Test deduplication (optional)
+git lfs dedup --test
+
+# Download the LFS files
+git lfs fetch
+
+# Create working tree files as clones of the files in the Git LFS storage directory using
+# copy-on-write functionality
+git lfs dedup
+```
+
+## Citation
+
+Please cite the following research paper when referencing this dataset:
+
+```
+@article{Scholler:2018apc,
+    author = {Sch\"oller, Friedrich and Skarke, Harald},
+    title = "{All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra}",
+    eprint = "1808.02422",
+    archivePrefix = "arXiv",
+    primaryClass = "hep-th",
+    doi = "10.1007/s00220-019-03331-9",
+    journal = "Commun. Math. Phys.",
+    volume = "372",
+    number = "2",
+    pages = "657--678",
+    year = "2019"
+}
+```