2D Hyperbolic Tilings By Infinite Tiles

*2223

Topology and geometry in H²

A line packing derived from the Voronoi partition of the *2223 3-fold forest with edge-length arccosh(3)

Tile-1-transitive

Surface reticulations

P surface reticulation

This hyperbolic line pattern wraps onto the P surface to give disjoint square 4-rings.

G surface reticulation

On the G surface, the hyperbolic lines map to geodesics that have the same arrangement in space as the channel structure of β-Manganese, β-Mn. The figures show the rod packing on the left and the induced partition of space on the right.

D surface reticulation

The line pattern projects onto the D surface to give geodesics with the same spatial structure as β-Tungsten, β-W. The figures show the rod packing on the left and the induced partition of space on the right.