Tetromino

A tetromino is a geometric shape composed of four squares, connected orthogonally. This, like dominoes and pentominoes, is a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.

A popular use of tetrominoes is in the video game Tetris, which refers to them under the name tetrimino.

Polyominos are formed by joining unit squares along their edges. A free polyomino is a polyomino considered up to congruence. That is, two free polyominos are the same if there is a combination of translations, rotations, and reflections that turns one into the other.

A free tetromino is a free polyomino made from four squares. There are five free tetrominoes (see figure).

One-sided tetrominoes are tetrominoes that may be translated and rotated but not reflected. They are used by, and are overwhelmingly associated with, the game Tetris. There are seven distinct one-sided tetrominoes. Of these seven, three have reflectional symmetry, so it does not matter whether they are considered as free tetrominoes or one-sided tetrominoes. These tetrominoes are:

The remaining four tetrominoes exhibit a phenomenon called chirality. These four come in two sets of two. Each of the members of these sets is the reflection of the other. The "L-polyominos":

The "skew polyominos":

As free tetrominoes, J is equivalent to L, and S is equivalent to Z. But in two dimensions and without reflections, it is not possible to transform J into L or S into Z.

The fixed tetrominoes allow only translation, not rotation or reflection. There are two distinct fixed I-tetrominoes, four J, four L, one O, two S, four T, and two Z, for a total of 19 fixed tetrominoes.

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