In 1974, Sir Roger Penrose proved that pentagons could be used to tessellate a plane, albeit in a manner that was non-regular (aperiodic). His first Penrose tile was comprised of pentagons, stars, boats and diamonds. His second featured non-regular quadrilaterals that looked like kites and darts.
1961
1974
In 1961, Hao Wang used “dominoes” to create a tessellation. The tiles (Wang Dominoes) were matched side by side according to their adjacent patterns. This seems simpler than it actually is!