Tetromino

A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners).^[1][2] Tetrominoes, like dominoes and pentominoes, are 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 created by the Soviet game designer Alexey Pajitnov, which refers to them as tetriminos.^[3] The tetrominoes used in the game are specifically the one-sided tetrominoes.

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.

One-sided tetrominoes are tetrominoes that may be translated and rotated but not reflected. They are used by, and are overwhelmingly associated with, Tetris. There are seven distinct one-sided tetrominoes. These tetrominoes are named by the letter of the alphabet they most closely resemble. The "I", "O", and "T" tetrominoes have reflectional symmetry, so it does not matter whether they are considered as free tetrominoes or one-sided tetrominoes. The remaining four tetrominoes, "J", "L", "S", and "Z", exhibit a phenomenon called chirality. J and L are reflections of each other, and S and Z are reflections of each other.

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:

"square tetromino"

"T-tetromino"

"L-tetromino"

"skew tetromino"

I

O

T

J

L

S

Z

The free tetrominoes (left side of line) have 11 dark squares and 9 light squares.
The one-sided tetrominoes (all 7 shown above) have 15 dark squares and 13 light squares.

A 5×4 board has 10 squares each color.
A 7×4 board has 14 squares each color.

Free tetrominoes in a rectangle with one hole

One-sided tetrominoes in a rectangle with two holes

Fixed tetrominoes in rectangle with one hole

Two sets of free tetrominoes in a 5×8 rectangle

Two sets of free tetrominoes in a 4×10 rectangle

Two sets of one-sided tetrominoes in a 8×7 rectangle

Two sets of one-sided tetrominoes in a 14×4 rectangle

I
"straight tetracube"

O
"square tetracube"

T
"T-tetracube"

L
"L-tetracube"

J is the same as L in 3D

S
"skew tetracube"

Z is the same as S in 3D

B
"Branch"

D
"Right Screw"

F
"Left Screw"