[math-fun] Aperiodic tiling of hyperbolic plane?

Has anyone worked out aperiodic tiles for the hyperbolic plane? Is there something analogous to Penrose tiles? Penrose tiles are a 2-d projection of a 5-d hypercube lattice; in 3d, there's a "cubic" tiling of hyperbolic space with dodecahedra where eight dodecahedra meet around a central vertex like cubes do in Euclidean space: http://reperiendi.files.wordpress.com/2011/01/dodecahedral.jpg If we took some "hypercubic" tiling of 5d hyperbolic space and projected down to 2d hyperbolic space, what would we get? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com