regfans

regfans is a Python library for studying lattice vector configurations, developed by Nate MacFadden at the Liam McAllister Group at Cornell.

Used by CYTools.

Core Functionality

The library computes and modifies regular triangulations of vector configurations. These could also be known as "regular polyhedral fans" or "vex triangulations".

Key capabilities:

• Verify properties of vector configurations (solid, totally-cyclic) and fans (fine, regular, point-configuration-compatible),
• Construct regular triangulations via lifting,
• Compute all (regular) triangulations via flip graph traversal, and
• Perform efficient linear flips.

See Triangulations: Structures for Algorithms and Applications by De Loera, Rambau, and Santos for a definitive reference on such topics. It is a wonderful book.

regfans has a lot of overlap with TOPCOM; regfans will port over more computations to TOPCOM as beneficial for speed (via triangulumancer).

Installation

Install via conda (most robust across platforms):

conda env create -f environment.yml
conda activate regfans
pip install -e .

Or via pip (see also PyPI listing):

pip install regfans

Note: Most methods require dual cone computation via pplpy. On macOS and Linux x86_64, pip install pulls a prebuilt pplpy wheel automatically (no system libraries needed). On other platforms (Windows, or ARM/musl Linux on older Pythons) there is no wheel and pip falls back to a source build that needs the ppl/gmp C libraries; the conda environment supplies those reliably.

Primary Interface

The main class is VectorConfiguration:

from regfans import VectorConfiguration

pts = [[1, -2, -1, -1], [1, 1, -1, 2], [-2, 0, 0, -1],
       [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]
vc = VectorConfiguration(pts)

# construct a regular triangulation via lifting
fan = vc.subdivide()
print(fan.is_fine(), fan.is_regular())

# compute all triangulations and the flip graph
all_fans = vc.all_triangulations()
G, fans, labels = vc.flip_graph(compute_node_labels=True)

See documentation/api.md for the full API reference and the tutorials directory for annotated examples.

Citation

If you are using regfans for toric-geometric or Calabi-Yau applications, please cite Calabi-Yau Threefolds from Vex Triangulations:

@article{MacFadden:2512.14817,
  author  = {MacFadden, Nate and Sheridan, Elijah},
  title   = {Calabi-{Y}au Threefolds from Vex Triangulations},
  doi     = {10.48550/arXiv.2512.14817},
  url     = {https://arxiv.org/abs/2512.14817},
}

Otherwise, please cite this repository:

@software{regfans,
  author  = {MacFadden, Nate},
  title   = {regfans},
  doi     = {10.5281/zenodo.19406101},
  url     = {https://github.com/natemacfadden/regfans},
  orcid   = {0000-0002-8481-3724},
}

This package was developed for constructing toric varieties in Calabi-Yau Threefolds from Vex Triangulations, supported in part by NSF grant PHY-2309456. Toric-geometric computations are provided by CYTools, which extends regfans via a vector_config module.

Organization

regfans/
├── src/regfans/
│   ├── vectorconfig.py   # VectorConfiguration class: triangulations, flip graph, VC properties
│   ├── fan.py            # Fan class: triangulation of a vector configuration
│   ├── circuits.py       # Circuit and Circuits classes
│   └── util.py           # shared utilities for vector configuration computations
├── tests/
│   ├── test_vectorconfig.py   # tests for VectorConfiguration
│   ├── test_fan.py            # tests for Fan
│   ├── test_circuits.py       # tests for circuits
│   └── test_util.py           # tests for utilities
├── tutorials/
│   ├── simple_lifting_ex.py   # constructing a regular triangulation via lifting
│   └── all_fans_ex.py         # computing all triangulations and the flip graph
├── documentation/
│   ├── api.md                 # full API reference
│   └── clean_api.py           # script to generate api.md
└── pyproject.toml