The Geometry Junkyard

Polyominoes and Other Animals

Connected subsets of the square lattice tiling of the plane are called polyominoes. These are often classified by their number of squares, so e.g. a tetromino has four squares and a pentomino has five; this nomenclature is by analogy to the word "domino" (a shape formed by two connected squares, but unrelated in etymology to the roots for "two" or "square").

If a polyomino or a higher-dimensional collection of cubes forms a shape topologically equivalent to a ball, it is called an animal. A famous open problem asks whether any animal in three dimensions can be transformed into a single cube by adding and removing cubes, at each step remaining an animal (it is known that removal alone does not always work). Other related figures include polyiamonds (collections of equilateral triangles), polyabolos (collections of half-squares), and polyhexes (collections of regular hexagons).

From the Geometry Junkyard, computational and recreational geometry pointers.
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David Eppstein, Theory Group, ICS, UC Irvine.
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