In 1918, K. Reinhardt ([url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN316479497]Über die Zerlegung der Ebene in Polygone[/url], Inaugural-Disstertation, Univ. Frankfurt a.M., R. Noske, Borna and Leipzig) showed that there are only three types of convex hexagons which can be the tile in a monohedral (one-tile) tessellation

This applet shows a small portion of the Type 1, 2, and 3 tessellations, and allow you to change the angles and sides of the base hexagon.