Hyperbolic Space
two key properties

more room
parallel vs. equidistant
circumference is exponential, not geometric, with radius
angle of parallelism increases with distance
all cones can be the same size

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