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: ≥ 5.

Smallest rectangle (3x4):

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

1-2 | 0 | ||||

3 | 0 | 0 | |||

4 | 0 | 66P | 3232P | ||

5 | 0 | 0 | 168168P | 0 | |

6 | 0 | 6464P | 763763C | 81688168P | ? |

7 | 0 | 0 | 33143314C | 0 | ? |

8 | 0 | 500500C | 1395113951C | 317174317174C | ? |

9 | 0 | 0 | ≥1≥1C | 0 | ? |

10 | 0 | 34923492C | ≥1≥1C | ≥1≥1C | ? |

11 | 0 | 0 | ≥1≥1C | 0 | ? |

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

Smallest prime reptiles (2Ix3, 4Zx2):

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

I domino | 0 | 0 | 64P | 13951P | ≥1P |

Z tetromino | 0 | 9P | 24964P | ≥194630401C | ≥1P |

Smallest common multiple (area 4):

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

solutions | 1P |