If you want to get an intuition for the weirder curvatures of 3D space, there's a playable "curved space simulator" created by topologist Jeff Weeks called Curv

If you want to get an intuition for the weirder curvatures of 3D space, there's a playable "curved space simulator" created by topologist Jeff Weeks called Curved Spaces. I remember it from a while back, but apparently it recently got an update! Some combinations of curvatures and tilings get really funky to navigate. http://www.geometrygames.org/CurvedSpaces/index.html.en http://www.geometrygames.org/CurvedSpaces/index.html.en