The 15 Pentagonal Tilings 12x18 Poster

There are only 15 possible pentagons that will tile the plane. Mathematician Karl Reinhardt found the first five in 1918. Fifty years later, R. B. Kershner found 3 more (06-08) and was satisfied that no more could be found. But then Richard E. James found another in 1975 (10). Non-mathematician Marjorie Rice found four more by 1977 (09, 11, 12, 13). In 1985, Rolf Stein found the 14th. In 2015, a 15th and final irregular pentagon was discovered using computer algorithm by Jennifer McCloud-Mann and Casey Mann, along with graduate student David von Derau. Then in 2017, Michaël Rao proved that only 15 exist and the search was over. The lighter-colored highlighted tile groups represent each type’s “primitive unit,” the smallest possible section of the tiling that generates the whole tesselation.

Museum-quality posters made on thick matte paper.