I think you could actually approximate an unobstructed hyperbolic plane to arbitrary precision with portals. In this game, the hyperbolic plane is represented a

I think you could actually approximate an unobstructed hyperbolic plane to arbitrary precision with portals. In this game, the hyperbolic plane is represented as a tiling of hexagons and heptagons: https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s If you take this model but upgrade each cell to a little 3D euclidean region, then you could completely surround it by portals that connect it to the neighbouring cells. The edges of the portals wouldn't be visible. The smaller the euclidean cells, the better the approximation to the hyperbolic plane.