The hyperbolic plane
can be modeled in a variety of ways, each construction revealing different
qualities of this surface. In the hyperbolic soccer ball model the
(five sided) pentagons of the classic soccer ball are replaced by
(seven sided) heptagons forcing the creation of a surface that curves
out rather than in.
In the polyhedral annular model,
thin strips are taped together, fanning out from a central point
to reveal the exponential expansion of hyperbolic space.