Hyperbolic Space
two key properties

more room
parallel vs. equidistant
circumference is exponential, not geometric, with radius
angle of parallelism increases with distance

outsider view
infinite space drawn in a finite projection
focus+context

may seem contradictory, but follows from definition of distance
triangles with < 180 degrees
pentagons with 5 right angles
Euclid's parallel postulate doesn't hold