A polyomino is a polygon constructed by joining together one or more unit squares edge to edge, such that no two edges coincide (equivalently, the only self-intersections allowed are doubled vertices). Polyominoes are named by size, or number of constituent unit squares, using Greek prefixes: size 2 is the domino, size 3 is the trominoes, size 4 the tetrominoes, etc. For heptominoes and above, polyominoes may have holes and are therefore may not be simply connected polyominoes; some do not consider these valid.
The enumeration of polyominoes of a given size has long interested mathematicians, and is generally considered a hard problem.
Polyominoes are a popular subject in recreational mathematics and the design of certain puzzles and games. The video game Tetris is based on the tetrominoes. It is well-known that the 12 pentominoes (selecting one enantiomorph each for chiral figures) can perfectly tile a 6 × 10 rectangle, among others.