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: ≥ 38.

Smallest known rectangle (3x10):

Smallest square (10x10):

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 |
---|---|---|---|---|---|---|---|---|---|---|

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

2 | ?? | 00 | ||||||||

3 | ?? | ?? | 00 | |||||||

4 | ?? | ?? | 00 | 00 | ||||||

5 | ?? | ?? | 00 | 00 | 00 | |||||

6 | ?? | ?? | 00 | 00 | 00 | 00 | ||||

7 | ?? | ?? | 00 | 00 | 00 | 00 | 00 | |||

8 | ?? | ?? | 00 | 00 | 00 | 00 | 00 | 00 | ||

9 | ?? | ?? | 00 | 00 | 00 | 00 | 00 | 00 | 00 | |

10 | ?? | ?? | 22P | 00 | 1010 | 2222 | 3636 | 180180 | 810810 | 33703370 |

11 | ?? | ?? | 00 | 00 | 1212 | 00 | 00 | 00 | 00 | 77107710 |

12 | ?? | ?? | 00 | 00 | 44 | 00 | 00 | 00 | 00 | ≥1≥1 |

13 | ?? | ?? | 00 | 00 | 88 | 00 | 00 | 00 | 00 | ≥1≥1 |

14 | ?? | ?? | 00 | 00 | 5656 | 00 | 00 | 00 | 00 | ≥1≥1 |

15 | ?? | ?? | 00 | 22 | 4040 | 6060 | 736736 | 90169016 | 8657286572 | ≥1≥1 |

16 | ?? | ?? | 00 | 00 | 1818 | 00 | 00 | 00 | 00 | ≥1≥1 |

17 | ?? | ?? | 00 | 00 | 2424 | 00 | 00 | 00 | 00 | ≥1≥1 |

18 | ?? | ?? | 00 | 00 | 6464 | 00 | 00 | 00 | 00 | ≥1≥1 |

19 | ?? | ?? | 00 | 00 | 100100 | 00 | 00 | 00 | 00 | ≥1≥1 |

20 | ?? | ?? | 44 | 22 | 418418 | 13821382 | 2175621756 | ≥1≥1 | ≥1≥1 | ≥1≥1 |

Smallest prime reptiles (5Ux4, 5Yx4):

polyomino \ n² | 1² | 2² | 3² | 4² | 5² | 6² | 7² |
---|---|---|---|---|---|---|---|

U pentomino | 0 | 0 | 0 | 2 | 1926 | 76235 | ≥16000 |

Y pentomino | 0 | 0 | 0 | 1 | 1303 | 83587 | ≥350000 |