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: ≥ 23.

Smallest known rectangle (8x10):

Smallest known 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 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | ?? | ||||||||||||||

2 | ?? | ?? | |||||||||||||

3 | ?? | ?? | ?? | ||||||||||||

4 | ?? | ?? | ?? | ?? | |||||||||||

5 | ?? | ?? | ?? | ?? | ?? | ||||||||||

6 | ?? | ?? | ?? | ?? | ?? | ?? | |||||||||

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

8 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | |||||||

9 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ||||||

10 | ?? | ?? | ?? | ?? | ?? | ?? | 00 | 22P | 44P | 66P | |||||

11 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 44 | ?? | ||||

12 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 44 | ?? | ?? | |||

13 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 66 | ?? | ?? | ?? | ||

14 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 66 | ?? | ?? | ?? | ?? | |

15 | ?? | ?? | ?? | ?? | ?? | ?? | 00 | 22 | 00 | 1818 | 44 | 2626 | 4040 | 8282 | 376376 |

16 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 2424 | ?? | ?? | ?? | ?? | 668668 |

17 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 20962096 |

18 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

19 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

20 | ?? | ?? | ?? | ?? | ?? | ?? | 00 | 88 | 5252 | ?? | 192192 | 574574 | ?? | ?? | ?? |

21 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

22 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

23 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

24 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? |

25 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | 1818 | 110110 | ?? | ?? | ?? | ?? | ?? | ?? |

Smallest prime reptiles (5Tx8, 5Wx8):

polyomino \ n² | 1² | 2² | 3² | 4² | 5² | 6² | 7² | 8² | 9² |
---|---|---|---|---|---|---|---|---|---|

T pentomino | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 60P | ≥1P |

W pentomino | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16P | ≥11000P |

Smallest common multiple (area 70):

Smallest common multiple without holes (area 80):

area | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

solutions | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ≥1 | ? | ≥1 |