Polyrects are formed by joining unit rectangles to form larger pieces.
The pieces are closely related to the polyominoes, having a short and a long version of each polyomino which is not the same by reflection in a mirror set diagonally to the square grid. If all long or short pieces are discarded, the remaining pieces are equivalent to the polyominoes.
Monorect - 1 (1 tile)
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Direct - 2 (4 tiles)
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| 1 | 2 |
Trirects - 3 (9 tiles)
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| 1 | 2 | 3 |
Tetrarects - 9 (36 tiles)
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| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
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| 8 | 9 |
Pentarects - 21 (105 tiles)
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| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Long I | Short I | Long L | Short L | Long Y | Short Y | Long T |
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| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| Short T | Long F | Short F | Long N | Short N | Long Z | Short Z |
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| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| Long P | Short P | Long U | Short U | V | X | W |
For higher orders of polyrects, the number of pieces is as follows:
Hexarects - 68
Heptarects - 208
Octarects - 730
Ennearects - 2542
Decarects - 9287