Hyperbolic space is a three-dimensional space whose geometry is non-Euclidean.This space can be tiled by regular dodecahedra (solids with 12 faces, each ofwhich is a pentagon) whose dihedral angles (that is, the angles betweenadjacent faces) are 90 degrees. Thus, these figures fit together as cubeswould in tiling ordinary, Euclidean three-space: four fit together at eachedge and eight at each vertex. Here is an artist's conception of thistiling as seen from the inside of one of the dodecahedra.
Hyperbolic Space Tiled with Dodecahedra, 1 by Charlie Gunn, 1990. Copyright by The GeometryCenter, University of Minnesota. Used with permission. This image is from the video "Not Knot" distributed by A.K.Peters, Wellesley, MA.
- Steven Weintraub
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