Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.

Prime rectangles: ≥ 0.

Smallest known rectangle (5x12):

Smallest square (12x12):

Blue number (*P*) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (*W*) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (*C*) - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 00 | ||||||||||||

2 | 00 | 00 | |||||||||||

3 | 00 | 00 | 00 | ||||||||||

4 | 00 | 00 | 00 | 00 | |||||||||

5 | 00 | 00 | 00 | 00 | 00 | ||||||||

6 | 00 | 00 | 00 | 00 | 00 | 00 | |||||||

7 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | ||||||

8 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | |||||

9 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 88 | 00 | ||||

10 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | |||

11 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 88 | 1010 | 22 | 00 | ||

12 | 00 | 00 | 00 | 00 | 22 | 00 | 00 | 4242 | 284284 | 44 | 302302 | ≥1000≥1000 | |

13 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 270270 | 4444 | 00 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

14 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 1616 | 00 | 232232 | ≥1000≥1000 | ≥1000≥1000 |

15 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 262262 | 284284 | 1414 | 330330 | ≥1000≥1000 | ≥1000≥1000 |

16 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | ≥1000≥1000 | ≥1000≥1000 | 8282 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

17 | 00 | 00 | 00 | 00 | 00 | 00 | 88 | ≥1000≥1000 | ≥1000≥1000 | 7070 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

18 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | 224224 | 364364 | 2626 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

19 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | ≥1000≥1000 | ≥1000≥1000 | 618618 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

20 | 00 | 00 | 00 | 00 | 00 | 00 | 00 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |