In the context of polyomino tiling, we define irregular to mean that the tiling has no rotational or reflectional symmetry, and that no subset of tiles within the tiling forms a rectangle.

We can apply this concept to rectifiable polyominoes. Here are some small irregular rectifiable polyominoes. These are minimal to the best of my knowledge.

poly-4-1

poly-4-2

poly-5-1

poly-5-2

poly-5-3

poly-6-1

poly-6-2

poly-7-1

poly-8-1

poly-8-2

We can also apply the concept to irreptiles. Here are some irregular irreptiles. These are also minimal.

rep-4-1

rep-4-2

rep-5-1

rep-5-2

rep-6-1

rep-7-1

rep-8-1

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