Polyomino in the context of "Pentomino"

A tile-based game is a game that uses tiles as one of the fundamental elements of play. Traditional tile-based games use small tiles as playing pieces for gambling or entertainment games. Some board games use tiles to create their board, giving multiple possibilities for board layout, or allowing changes in the board geometry during play.

Each tile has a back (undifferentiated) side and a face side. Domino tiles are usually rectangular, twice as long as they are wide and at least twice as wide as they are thick, though games exist with square tiles, triangular tiles and even hexagonal tiles. Modern games may use unconventional non-tileable shapes such as the curved-shaped Bendominoes, or use many different shapes that together tile a surface such as the polyominoes in Blokus.

In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes.

Solomon Wolf Golomb (/ɡəˈloʊm/ gə-LOHM; May 30, 1932 – May 1, 2016) was an American mathematician, engineer, and professor of electrical engineering at the University of Southern California, best known for his works on mathematical games. He most notably invented Cheskers (a hybrid between chess and checkers) in 1948. He also fully described polyominoes in 1953. He specialized in problems of combinatorial analysis, number theory, coding theory, and communications. Pentomino board games, based on his work, would go on to inspire Tetris.

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.