I'm currently working on a specialized game board, which will be a hyperbolic plane tiled with octagons, as a personal that I'm getting someone to crochet for me. Right now, the plan is to crochet a bunch of octagons and stitch them together. My (very rough and possibly inaccurate) models indicate that I will need four colours to tile the plane. At the moment, I'm wondering if the four colour theorem extends to hyperbolic space.
If it does not, then how many colours will I need?