Dehn
invariants of hyperbolic tiles. The Dehn invariant is one way
of testing whether a Euclidean polyhedron can be used to tile space.
But as Doug Zare describes, there are hyperbolic tiles
with nonzero Dehn invariant.
Gallery of interactive on-line geometry.
The Geometry Center's collection includes programs for generating
Penrose tilings, making periodic drawings a la Escher in the Euclidean
and hyperbolic planes, playing pinball in negatively curved spaces,
viewing 3d objects, exploring the space of angle geometries, and
visualizing Riemann surfaces.
Gaussian
continued fractions.
Stephen Fortescue discusses some connections between basic
number-theoretic algorithms and the geometry of tilings
of 2d and 3d hyperbolic spaces.
Hyperbolic geometry. Visualizations and animations including
several pictures of hyperbolic tessellations.
Hyperbolic
shortbread. The Davis math department eats a Poincaré model
of a tiling of the hyperbolic plane by 0-60-90 triangles.
The
hyperbolic surface activity page. Tom Holroyd describes hyperbolic
surfaces occurring in nature, and explains how to make a paper model of
a hyperbolic surface based on a tiling by heptagons.
