Not hyperbolic as in exaggerated, hyperbolic as in the geometry.
This means everything is fucked up and your normal understanding of reality as it is does not work;
Triangles can handle angles of zero. You can fit 5 or more squares around one vertex without overlap.
Infinite parallel lines.
Exponential area growth instead of cubed for spheres and whatnot. It even uses triple integrals for cubes. holy shit.
Spheres got it easy with the formula (for -1 curvature) of π(sinh(2r) - 2r) which loves to go boom in terms of a result;
A sphere with radius 1 (any unit here really) has a hyperbolic volume of around 5.111
With 5, however, it's at around 34,568. That is a 660% difference in volume of a normal sphere of radius 5.