---
license: mit
task_categories:
  - other
tags:
  - physics
  - string-theory
  - calabi-yau
  - algebraic-geometry
  - triangulation
size_categories:
  - 10M<n<100M
---

# CYTransformer — FRST training datasets

Favorable 4-dimensional reflexive polytopes paired with **Fine, Regular, Star Triangulations
(FRSTs)** — the combinatorial data behind smooth Calabi–Yau threefolds — pre-split into
train / validation / test.

These are the datasets behind *"Transforming Calabi–Yau Constructions: Generating New Calabi–Yau
Manifolds with Transformers"* ([arXiv:2507.03732](https://arxiv.org/abs/2507.03732)), released for
[**AICY**](https://aicy.physics.wisc.edu).

Code: [github.com/jhtyip/cytransformer](https://github.com/jhtyip/cytransformer) ·
Weights: [jhtyip/cytransformer-frst-models](https://huggingface.co/jhtyip/cytransformer-frst-models)

## Contents

One folder per configuration. `9+1` means 9 polytope vertices plus the origin; the paper's
N<sub>vert</sub> counts the origin, so folder `9+1` is the paper's N<sub>vert</sub> = 10.

| Folder | h<sup>1,1</sup> | Train | Val | Test | Size | Sampling |
|---|---|---|---|---|---|---|
| `9+1`  | 5  | 3,897 / 45,416     | 500 / 5,763     | 500 / 5,535     | 20 MB   | exhaustive |
| `10+1` | 6  | 14,608 / 513,973   | 1,000 / 36,213  | 1,000 / 34,095  | 242 MB  | exhaustive |
| `11+1` | 7  | 42,221 / 5,266,151 | 3,000 / 347,784 | 3,000 / 376,398 | 2.88 GB | exhaustive |
| `12+1` | 8  | 7,425 / 3,751,111  | 1,000 / 503,231 | 1,000 / 488,398 | 2.60 GB | exhaustive |
| `13+1` | 9  | 16,727 / 4,386,161 | 1,000 / 260,805 | 1,000 / 258,880 | 3.03 GB | fast sampler, ≤300 per polytope |
| `14+1` | 10 | 16,486 / 4,815,210 | 1,000 / 291,089 | 1,000 / 291,313 | 3.72 GB | fast sampler, ≤300 per polytope |

Train / val / test columns are *polytopes / pairs*. **Every count above was measured from the files**,
not taken from filenames. Splits are per-polytope, so no polytope appears in more than one split.

## Format

Six files per folder — `{polys,triangs}_{train,val,test}` — as plain JSON lists of
`[POLYID, STRING]` records. Row *i* of the polys file pairs with row *i* of the triangs file, so a
polytope is repeated once per triangulation.

```json
polys:   [3081, "{{0,1,0,0},{1,0,0,0},{-3,-2,-1,-1},{0,0,0,1},{0,0,1,0},{-2,0,-1,0},{-1,0,1,-1},{-1,1,0,0},{-2,-1,0,-1}}"]
triangs: [3081, "{{0,1,2,5},{0,1,2,8},{0,1,3,4},{0,1,3,5},{0,1,4,6},{0,1,6,8},{0,2,5,8},...}"]
```

A **polytope** is its list of vertices in ℤ⁴ (`DRESVERTS`). A **triangulation** is its list of
4-simplices, each given as indices into that vertex list. Polytopes are *favorable* — vertex count
equals lattice-point count minus the origin.

Because each polytope is duplicated once per triangulation, these files compress extremely well
(the polys files by more than 100×).

## Usage

```python
from huggingface_hub import hf_hub_download
p = hf_hub_download("jhtyip/cytransformer-frst-datasets", "9+1/9+1_polys_train.json", repo_type="dataset")
t = hf_hub_download("jhtyip/cytransformer-frst-datasets", "9+1/9+1_triangs_train.json", repo_type="dataset")
```

They feed `cyt-train` directly — the files are already split, so no preparation step is needed.

## Provenance

Generated with [CYTools](https://cy.tools) from the Kreuzer–Skarke database. Configurations
`9+1`–`12+1` enumerate triangulations exhaustively; `13+1` and `14+1` use a fast sampler capped at
300 triangulations per polytope, since exhaustive enumeration is infeasible at that size.

Published filenames drop the polytope counts that appeared in the original working filenames —
those counts referred to scan ranges and configured limits rather than file contents, and did not
match the data. The measured counts are in the table above.

## Citation

```bibtex
@article{Yip:2025hon,
  author  = {Yip, Jacky H. T. and Arnal, Charles and Charton, Fran\c{c}ois and Shiu, Gary},
  title   = {Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers},
  journal = {arXiv e-prints},
  eprint  = {2507.03732},
  year    = {2025},
  doi     = {10.48550/arXiv.2507.03732}
}
```

MIT licensed. Department of Physics, University of Wisconsin–Madison.