tetrominoes

Tetrominoes are polyominoes formed by four unit squares that share edges. The term combines the Greek tetra- meaning four with -omino, a shape. Tetrominoes are the simplest four-square polyominoes and are studied in tiling theory and recreational mathematics. They gained worldwide recognition from the puzzle game Tetris, which uses seven distinct tetrominoes that can be rotated and dropped to form complete lines.

There are seven tetrominoes commonly used in Tetris, labeled I, O, T, S, Z, J, and L. The I tetromino is a straight line of four squares; the O tetromino is a 2×2 square; the T forms a T shape; S and Z are skewed zigzags; J and L are mirror-image stair shapes. In terms of orientation, most tetrominoes have multiple distinct rotations: I has two orientations, O has one, T has four, S and Z have two, and J and L each have four. If reflections are considered identical, there are five free tetromino shapes rather than seven.

Beyond games, tetrominoes appear in tiling problems, puzzle design, and algorithmic packing. They provide simple yet rich examples for questions about covering regions, parity, and colorings on the square lattice. The study of tetrominoes originated with Solomon W. Golomb and his work on polyominoes in the 1950s, and it remains a basic topic in combinatorics and recreational mathematics.