Here is C# code to generate various semi-regular hyperbolic tesselations.

Hyperbolic tiling.gh (18.1 KB)

It currently outputs quite a lot of duplicates, I will try to clean this when I have time.

The code first generates a regular polygon, and then transforms it into a hyperbolic polygon with the same vertices. The planar radii of these curved polygons are found through an equation :

\sqrt{\frac{\sin^2 \frac{\pi}{n}}{\cos^2 \frac{\pi}{p} - \sin^2 \frac{\pi}{n}}}

where n is the number of sides of the starting polygon, and p is the number of polygons meeting at each vertex.

All these transformations are then looped to get the uniform tesselation.

More info https://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane