Polyomino

All 18 pentominos

A polyomino is a geometric figure consisting of one or more equally-sized squares, connected edge to edge.

The number of unique polyominos for a given number of squares is based on the rules at which they're constructed:

• Free polyominos may be translated, rotated, reflected.
• One-side polyominos may be translated or rotated.
• Fixed polyominos may only be translated.
• Polyominos of size 7 or higher may have "holes", which may be included or excluded on a given count.

Polyomino puzzles

Polyominos are used in recreational mathematics, such as trying to compose a large shape from a given set of polyominos.

These can be solved using methods similar to the Exact Cover problem, solvable using algorithms such as Kunth's Algorithm X.