Polyrects

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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)

           

  Direct - 2 (4 tiles)

         
1 2          

  Trirects - 3 (9 tiles)

       
1 2 3        

  Tetrarects - 9 (36 tiles)

1 2 3 4 5 6 7
         
8 9          

  Pentarects - 21 (105 tiles)

1 2 3 4 5 6 7
Long I Short I Long L Short L Long Y Short Y Long T
8 9 10 11 12 13 14
Short T Long F Short F Long N Short N Long Z Short Z
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

 

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