History
Karl Reinhardt (1918) found the 5 pentagon tilings that are "tile transitive", meaning that the automorphism group acts transitively on the tiles. R. B. Kershner (1968) found 3 more tilings, and claimed incorrectly that this list was complete. Richard E. James III found a 9th tiling in 1975, after reading about Kershner's results in Martin Gardner's Mathematical Games column of July 1975 (reprinted in (Gardner 1988)). Schattschneider (1978) described how Marjorie Rice, an amateur mathematician, discovered four new types of tessellating pentagons in 1976 and 1977. Schattschneider (1985) described a 14th tiling found by Rolf Stein in 1985. O. Bagina (2011) (in Russian) proved 8 edge-to-edge convex types, a result obtained independently by T. Sugimoto in 2012.
Read more about this topic: Pentagon Tiling
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