Polyomino
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Polyominoes are shapes made from a finite number(side-to-side connected) unit squares on the standard plane. The following pairs of squares are not side-side connected:
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The following pair is side-side connected:
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Types of Polyomino
[edit]n | name | number of free polyominoes | number of free polyominoes with holes | number of one-sided polyominoes | = number of fixed polyominoes |
---|---|---|---|---|---|
1 | monomino | 1 | 0 | 1 | 1 |
2 | domino | 1 | 0 | 1 | 2 |
3 | tromino/triomino | 2 | 0 | 2 | 6 |
4 | tetromino | 5 | 0 | 7 | 19 |
5 | pentomino | 12 | 0 | 18 | 63 |
6 | hexomino | 35 | 0 | 60 | 216 |
7 | heptomino | 108 | 1 | 196 | 760 |
8 | octomino | 369 | 6 | 704 | 2,725 |
9 | nonomino | 1,285 | 37 | 2,500 | 9,910 |
10 | decomino | 4,655 | 195 | 9,189 | 36,446 |
11 | undecomino | 17,073 | 979 | 33,896 | 135,268 |
12 | dodecomino | 63,600 | 4,663 | 126,759 | 505,861 |
A polyomino made from three squares is a tromino. There are only two possible trominoes:
![](https://upload.wikimedia.org/wikipedia/commons/9/9e/TrominoI.jpg)
![](https://upload.wikimedia.org/wikipedia/commons/3/3f/TrominoV.jpg)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Tetromino_Tiling_5x8.svg/240px-Tetromino_Tiling_5x8.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Tetromino_Tiling_4x10.svg/300px-Tetromino_Tiling_4x10.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/All_18_Pentominoes.svg/550px-All_18_Pentominoes.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Pentomino_Naming_Conventions.svg/400px-Pentomino_Naming_Conventions.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/0/09/Pentomino_Puzzle_Solutions.svg/400px-Pentomino_Puzzle_Solutions.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/47/Pentomino_Cube_Solutions.svg/420px-Pentomino_Cube_Solutions.svg.png)
The 35 free hexominoes | The 11 cubic nets |
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Heptominoes.svg/720px-Heptominoes.svg.png)
![]() 90° reflection |
![]() 45° reflection |
![]() Rotation |
![]() Both |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/All_369_free_octominoes.svg/750px-All_369_free_octominoes.svg.png)
![]() 90° reflection |
![]() 45° reflection |
![]() C2 rotation |
![]() C4 rotation |
![]() Both |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Permutominoes_2x2.svg/760px-Permutominoes_2x2.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Permutominoes_3x3.svg/740px-Permutominoes_3x3.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Ferrer_partitioning_diagrams.svg/430px-Ferrer_partitioning_diagrams.svg.png)