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Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Create a graph of a regular hyperbolic tiling
ResourceFunction["RegularHyperbolicTilingGraph"][n,m,k] generates a graph corresponding to a tiling of the hyperbolic plane where m regular n-gons share a vertex, propagated for k steps. |
"Beltrami" | embed graph on the Beltrami-Klein disk |
"HalfPlane" | embed graph on the Poincaré half-plane |
"Hemisphere" | embed graph on a hemisphere (stereographic projection of Poincaré disk) |
"Hyperboloid" | embed graph in the hyperboloid (Minkowski) model |
"Poincare" | embed graph on the Poincaré disk |
Graph of a {5,4} regular hyperbolic tiling:
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Show the graph in 3D:
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Show the steps in generating a {6,4} regular hyperbolic tiling, embedded on the Poincaré disk:
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Embed the graph in the Beltrami-Klein disk:
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Embed the graph in the Poincaré disk:
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Embed the graph in the Poincaré half plane:
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Embed the graph in the hemisphere:
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Embed the graph in a hyperboloid:
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Use an embedding supported by Graph:
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RegularHyperbolicTilingGraph returns unevaluated if the arguments do not correspond to a valid regular hyperbolic tiling:
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For moderately sized arguments, generating the graph might take a long time:
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This work is licensed under a Creative Commons Attribution 4.0 International License