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

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

Prime rectangles: ≥ 81.

Smallest rectangle and smallest square (3x3):

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

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

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

3 | 00 | 00 | 44 | ||||||||

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

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

6 | 00 | 00 | 1616 | 00 | 22 | 260260 | |||||

7 | 00 | 00 | 00 | 00 | 00 | 44 | 00 | ||||

8 | 00 | 00 | 00 | 00 | 00 | 6868 | 00 | 00 | |||

9 | 00 | 00 | 6464 | 00 | 00 | 42444244 | 5252 | 22 | 284272284272 | ||

10 | 00 | 00 | 00 | 00 | 00 | 138138 | 88 | 11801180 | 1047410474 | 99709970 | |

11 | 00 | 00 | 00 | 00 | 00 | 16921692 | 11161116 | 25682568 | 732732 | 6425464254 | 469480469480 |

12 | 00 | 00 | 256256 | 00 | 22 | 6933269332 | 1597815978 | 2137821378 | ≥1≥1 | ≥1≥1 | ≥1≥1 |

13 | 00 | 00 | 00 | 00 | 3232 | 35283528 | 568568 | 1304813048 | ?? | ?? | ?? |

14 | 00 | 00 | 00 | 00 | 88 | 3717037170 | 12621262 | 2240622406 | ?? | ?? | ?? |

15 | 00 | 00 | 10241024 | 00 | 00 | 11329721132972 | 85248524 | ≥1≥1 | ?? | ?? | ?? |

16 | 00 | 00 | 00 | 00 | 00 | 7977079770 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

17 | 00 | 00 | 00 | 00 | 00 | 763216763216 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

18 | 00 | 00 | 40964096 | 00 | 140140 | 1851963418519634 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

19 | 00 | 00 | 00 | 00 | 256256 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

20 | 00 | 00 | 00 | 00 | 6464 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

21 | 00 | 00 | 1638416384 | 00 | 00 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

22 | 00 | 00 | 00 | 00 | 00 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

23 | 00 | 00 | 00 | 00 | 28882888 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

24 | 00 | 00 | 6553665536 | 00 | 1574015740 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

25 | 00 | 00 | 00 | 00 | 2518425184 | ≥1≥1 | ≥1≥1 | ≥1≥1 | ?? | ?? | ?? |

Smallest prime reptiles (4Tx3, 5Ux3):

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

T tetromino | 0 | 0 | 256P | 0 | 162P | ≥4815104840P | ≥1P |

U pentomino | 0 | 0 | 1024P | 0 | 21418P | ≥1251927258400P | ≥1P |

Smallest common multiple (area 40):

area | 20 | 40 |
---|---|---|

solutions | ? | ≥1 |