2D Hyperbolic Tilings By Infinite Tiles

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Topology and geometry in H²

Forest of 4-fold trees with edge-length arccosh(5)

Tile- and Vertex-1-transitive

Surface reticulations

P surface reticulation
The forest of 4-fold trees projects onto the P surface to give a graph with infinitely many parallel laminar components. Each component is a square grid.
D surface reticulation

The four-coordinated forest projected onto the D surface gives two interpenetrating diamond nets. This is exactly the same structure as the labyrinth graph of the D surface.