Yes, I used the Poincaré half-plane model for the 3-dimensional hyperbolic space. I put a square lattice on the plane z=0 such that when you reduce modulo this lattice, the boundary becomes a flat torus, which is why I embedded this hyperbolic quotient space as a torus inside R^3. The project is open-source, but it might be a bit complicated to get some intuition from the code, maybe one day I'll make an explanation video.
