According to Wikipedia: << There are no finite-faceted regular tessellations of hyperbolic space of dimension 5 or higher. There are 5 regular honeycombs in H5 with infinite (Euclidean) facets or vertex figures: {3,4,3,3,3}, {3,3,4,3,3}, {3,3,3,4,3}, {3,4,3,3,4}, {4,3,3,4,3}.

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So it appears that the choices are severely limited. --Dan Mike Stay wrote: << 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?

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Those who sleep faster get more rest.