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: 11.

Smallest rectangles (3x8, 4x6):

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 | N>0 |
---|---|---|---|---|---|---|---|---|

1-2 | 0 | |||||||

3 | 0 | 0 | ||||||

4 | 0 | 00 | 00 | |||||

5 | 0 | 0 | 00 | 0 | ||||

6 | 0 | 0 | 1616P | 0 | 2627226272P | |||

7 | 0 | 0 | 240240P | 0 | 0 | 0 | ||

8 | 0 | 1616P | 23202320P | 151740151740P | 68201966820196C | ≥1≥1C | ≥1≥1C | |

9 | 0 | 0 | 1697016970P | 0 | 0 | 0 | ≥1≥1C | 4k |

10 | 0 | 0 | 113902113902P | 0 | ≥1≥1C | 0 | ≥1≥1C | 2k |

11 | 0 | 0 | 674488674488P | 0 | 0 | 0 | ≥1≥1C | 4k |

12 | 0 | 58125812P | 37914143791414C | 779579633779579633P | ≥1≥1C | ≥1≥1C | ≥1≥1C | all |

13 | 0 | 0 | 2041767820417678C | 0 | 0 | 0 | ≥1≥1C | 4k |

14 | 0 | 0 | ≥1≥1C | 0 | ≥1≥1C | 0 | ≥1≥1C | 2k |

15 | 0 | 0 | ≥1≥1C | 0 | 0 | 0 | ≥1≥1C | 4k |

16 | 0 | 616284616284C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | all |

17 | 0 | 0 | ≥1≥1C | 0 | 0 | 0 | ≥1≥1C | 4k |

18 | 0 | 0 | ≥1≥1C | 0 | ≥1≥1C | 0 | ≥1≥1C | 2k |

19 | 0 | 0 | ≥1≥1C | 0 | 0 | 0 | ≥1≥1C | 4k |

20 | 0 | 4309530243095302C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | all |

N>0 | x | 4k | all | 4k | 2k | 4k | all |

Smallest prime reptiles (4Ix3, 4Ox3, 4Lx3, 4Tx3, 4Zx3):

polyomino \ n² | 1² | 2² | 3² |
---|---|---|---|

I tetromino | 0 | 0 | 5812P |

L tetromino | 0 | 0 | 4386P |

O tetromino | 0 | 0 | 26272P |

T tetromino | 0 | 0 | 6730P |

Z tetromino | 0 | 0 | 2812P |

Smallest common multiple (area 32):

area | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 |
---|---|---|---|---|---|---|---|---|

solutions | 0 | ? | ? | ? | ? | ? | ? | ≥1 |

- Smallest known common multiple found by Livio Zucca (http://www.iread.it/lz/4chall.html)