A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). 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. The tetrominoes used in the game are specifically the one-sided tetrominoes. The tetrominoes Free 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. The free tetrominoes have the following symmetry: Straight: vertical and horizontal reflection symmetry, and two points of rotational symmetry Square: vertical and horizontal reflection symmetry, and four points of rotational symmetry T: vertical reflection symmetry only L: no symmetry S and Z: two points of rotational symmetry only One-sided 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. Fixed tetrominoes 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: Tiling a rectangle Filling a rectangle with one set of tetrominoes A single set of free tetrominoes or one-sided tetrominoes cannot fit in a rectangle. This can be shown with a proof similar