Pentomino

A pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different free pentominoes. When reflections are considered distinct, there are 18 one-sided pentominoes. When rotations are also considered distinct, there are 63 fixed pentominoes.

Pentomino tiling puzzles and games are popular in recreational mathematics. Usually, video games such as Tetris imitations and Rampart consider mirror refections to be distinct, and thus use the full set of 18 one-sided pentominoes.

Each of the twelve pentominoes satisfies the Conway criterion; hence every pentomino is capable of tiling the plane. Each chiral pentomino can tile the plane without reflecting it.

Pentominoes were formally defined by American professor Solomon W. Golomb starting in 1953 and later in his 1965 book Polyominoes: Puzzles, Patterns, Problems, and Packings. They were introduced to the general public by Martin Gardner in his October 1965 Mathematical Games column in Scientific American. Golomb coined the term "pentomino" from the Ancient Greek πέντε / pénte, "five", and the -omino of domino, fancifully interpreting the "d-" of "domino" as if it were a form of the Greek prefix "di-" (two). Golomb named the 12 free pentominoes after letters of the Latin alphabet that they resemble.

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