The distinctive nature of polyominoes
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Dissections usually start from a geometric shape that, through some clever cutting, yields other shapes. The story of polyominoes — and of pentominoes in particular — is different: only after counting and identifying a set of pieces do you then try to reconstruct a given geometric figure.
As early as 1907, Henry Dudeney had identified figures made up of five squares joined along at least one side (The Canterbury Puzzles, Dover, 1958). André Sainte-Laguë had developed the more general study of polyominoes in his notebooks on combinatorial analysis (held in the archives of the Conservatoire des arts et métiers), around 1925 — a trailblazer who worked entirely by hand, without a computer.
The word polymino (or polyomino) was coined by Solomon Wolf Golomb (1932-2016) in 1953 to designate a planar configuration made up of congruent squares placed edge to edge. Two configurations are counted as one if one can be obtained from the other by a rotation or reflection. The order of a polyomino corresponds to the number of squares assembled to form a configuration.
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