Combinations of regular shapes into patterns by means of a set of predefined rules can be observed in many everyday situations, from the tiles on a bathroom floor, the hexagonal patterns of honeycombs, the games of dominoes and Tetris, or even chemical structures of molecules such as hydrocarbons. In all these examples the predefined rules consist of shapes, which abut one another by the contact of respective edges, leaving no interior holes. Interestingly, only three regular polygons can construct these two-dimensional patterns. When the polygons are squares the possible patterns have been called (square-cell) animals by Martin Gardner (1956) and polyominoes by Solomon Golomb (1965). The animals with four cells are the same as the tiles in the Tetris. As shown in Figure 1, the five animals with four cells have been called the names below them by Frank Harary (1982, 1983).
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