2D Hyperbolic Tilings By Infinite Tiles

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Topology and geometry in H²

3-fold tree with edge-length arccosh(3).

Tile- and Vertex-1-transitive.

Surface reticulations

P surface reticulation

This 3-fold forest of trees projects onto the P surface to form an array of isolated cubic clusters. In the figure below, the edges have been lifted off the P surface and straightened.

G surface reticulation

On the G surface, this 3-fold forest gives two interpenetrating chiral +Y* nets. Each net has symmetry P4(1)32, but the structure as a whole is I4(1)32.

D surface reticulation

Projecting the forest onto the D surface we obtain four interpenetrating +Y* nets.