metadata

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
tags:
  - physics
  - math

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. More information is available at the Calabi-Yau data website. The dataset can be explored using the search frontend.

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.

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:

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:

# 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"
}