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: 7.

Smallest rectangle (1x6):

Smallest square (4x4):

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

1 | 0 | |||||

2 | 00 | 00 | ||||

3 | 0 | 00 | 0 | |||

4 | 00 | 22P | 1414P | 108108C | ||

5 | 0 | 66P | 0 | 490490C | 0 | |

6 | 22P | 1717C | 146146C | 25392539C | 2218322183C | ? |

7 | 0 | 3434P | 0 | 1099410994C | 0 | ? |

8 | 33P | 8080C | 12691269C | 5248352483C | ≥1≥1C | ? |

9 | 0 | 165165C | 0 | ≥1≥1C | 0 | ? |

10 | 77P | 358358C | 1017110171C | ≥1≥1C | ≥1≥1C | ? |

11 | 0 | 724724C | 0 | ≥1≥1C | 0 | ? |

12 | 1111C | 15081508C | 7939379393C | ≥1≥1C | ≥1≥1C | ? |

13 | 0 | 30393039C | 0 | ≥1≥1C | 0 | ? |

14 | 2020C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ? |

15 | 0 | ≥1≥1C | 0 | ≥1≥1C | 0 | ? |

16 | 3232C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ≥1≥1C | ? |

17 | 0 | ≥1≥1C | 0 | ≥1≥1C | 0 | ? |

N>0 | 2k | all | 2k | all | 2k |

Smallest prime reptiles (2Ix2, 4Ix2):

polyomino \ n² | 1² | 2² | 3² | 4² |
---|---|---|---|---|

I domino | ? | ?P | ?P | ?C |

I tetromino | ? | ?P | ?P | ?C |

Smallest common multiple (area 4):

area | 4 |
---|---|

solutions | 1P |