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 and smallest square (6x6):

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 | 22 | |||||||

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

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

9 | 00 | 00 | 00 | 00 | 00 | 22 | 00 | 00 | 00 | ||||

10 | 00 | 00 | 00 | 00 | 00 | 88 | 22 | 66 | 1616 | 318318 | |||

11 | 00 | 00 | 00 | 00 | 00 | 1414 | 44 | 1818 | 1212 | 648648 | 648648 | ||

12 | 00 | 00 | 00 | 00 | 00 | 44 | 66 | 88 | 2626 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | |

13 | 00 | 00 | 00 | 00 | 00 | 2626 | 88 | 3434 | 2020 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

14 | 00 | 00 | 00 | 00 | 00 | 6464 | 1010 | 150150 | 188188 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

15 | 00 | 00 | 00 | 00 | 00 | 6464 | 88 | 474474 | 228228 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

16 | 00 | 00 | 00 | 00 | 00 | 7474 | 2222 | 340340 | 972972 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

17 | 00 | 00 | 00 | 00 | 00 | 296296 | 3232 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

18 | 00 | 00 | 00 | 00 | 00 | 464464 | 7474 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

19 | 00 | 00 | 00 | 00 | 00 | 492492 | 104104 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |

20 | 00 | 00 | 00 | 00 | 00 | 964964 | 190190 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 | ≥1000≥1000 |