The tilings shown use as few tiles as I know how, and are not necessarily unique under this condition. If you find a tiling with fewer tiles, please write.
Most of these solutions were found by Karl Scherer, who published them in A Puzzling Journey to the Reptiles in 1986. The third hexabolo solution was found independently by Bryce Herdt in 2009.
See also Similar Polyaboloes Tiling an Octagon.
Last revised 2018-09-06.