A fixed polyomino is a polyomino considered up to translation only. Moving a finite side-connected square-lattice shape does not change it, but rotating or reflecting it may produce a different fixed shape.
There are two fixed dominoes, horizontal and vertical, although they form one free polyomino class. A fixed square tetromino remains the same under quarter-turn rotation because it already has that symmetry. Thus the word fixed records which transformations are identified, rather than prohibiting a shape from having symmetries.
One can represent a fixed polyomino by a finite set of lattice cells and translate it so the minimum horizontal and vertical coordinates are both zero. This removes positional redundancy for enumeration; connectivity along whole cell sides remains part of the polyomino definition.
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