User:Tomruen/Versatile (geometry)

In geometry, a versatile is a polygon that can express a monohedral tiling in many possible ways, periodically or aperiodically. The polygons may be equilateral or not, convex or not, connected edge-to-edge or not. The regular polygons, the square, equilateral triangle and regular hexagon do not qualify as a versatile because they only self-tile in one way.

The term was coined by Michael Hirschhorn in 1977, and used in 1979 by Branko Grünbaum and Geoffrey Colin Shephard in spiral tilings and expanded in 1981 by Marjorie Rice and Doris Schattschneider. for wider aperiod tiles.

All examples below are selected to each be able to fill a regular polygon, although that is not a requirement.