2D Hyperbolic Tilings By Infinite Tiles


Topology and geometry in H²

3-fold tree with edge-length arccosh(5)

Tile-1- and Vertex-1-transitive

Surface reticulations

P surface reticulation

On the P surface, this 3-fold tree projects to 8 identical interpenetrating +Y* nets.

G surface reticulation
On the G surface, we obtain two interpenetrating Y* nets, but in a different embedding from those from the *2223 3-fold tree.

D surface reticulation

The forest of 3-fold trees projects onto the D surface to give an array of isolated tetrahedra. Each tetrahedra encloses a node of one of the diamond nets that form the labyrinth graph of the D surface.