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hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices

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hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincare disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs.


hypertiling is available in the PyPI package index and can be installed using

$ pip install hypertiling

For optimal performance, we highly recommand to use hypertiling together with python-numba, which, if not already present on your system can be installed automatically using the [numba]-suffix, i.e.

$ pip install hypertiling[numba]

The package can also be locally installed from our public git repository via

$ git clone
$ pip install .


In Python, import tiling object from the hypertiling library

from hypertiling import HyperbolicTiling

Set parameters, initialize and generate the tiling

p = 7
q = 3
nlayers = 5

T = HyperbolicTiling(p,q,nlayers) 

Further examples are available in our documentation and Jupyter demo notebooks.


This project is developed at:
Institute for Theoretical Physics and Astrophysics
University of Wuerzburg


If you use hypertiling, we encourage you to cite or reference this work as you would any other scientific research. The package is a result of a huge amount of time and effort invested by the authors. Citing us allows us to measure the impact of the research and encourages others to use the library.

Cite us:

Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson S.E. Portela, Dietmar Herdt and Felix Dusel. (2023). The hypertiling project. Zenodo.



The core functionality of the package is the generation of regular hyperbolic tilings projected onto the Poincare disk. Tilings in the upper row are centered about a cell, in the lower row about a vertex.


The hypertiling package allows to perform triangle refinements, such as shown here


Hyperbolic Magnet

Simulation of a Ising-like Boltzmann spin model with anti-ferromagnetic interactions on a hyperbolic (7,3) tiling, quenched at low temperature. The hyperbolic antiferromagnet (left) exhibits geometrical frustration, whereas on a flat lattice (right) an ordered anti-parallel alignment can be observed.

Helmholtz Equation

Solution of an electrostatic Helmholtz problem on a refined (3,7) tiling, where boundary values have been fixed to either -1 (red) or +1 (blue). One readily recognizes a field value separation according to geodesic arcs in the Poincare disk representation of the hyperbolic plane.

Further information and examples can be found in our Jupyter notebooks in /examples subfolder.


Every part of hypertiling is available under the MIT license.

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