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 (4x5):

Smallest square (8x8):

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 | 1-3 | 4 | 5 | 6 | 7 | 8 | N>0 |
---|---|---|---|---|---|---|---|

1-3 | 0 | ||||||

4 | 0 | 00 | |||||

5 | 0 | 22P | 00 | ||||

6 | 0 | 44P | 00 | 00 | |||

7 | 0 | 66P | 00 | 00 | 00 | ||

8 | 0 | 88P | 4646C | 100100C | 180180C | 602602C | |

9 | 0 | 1616P | 00 | 00 | 00 | 29882988C | ? |

10 | 0 | 3232C | 00 | 00 | 00 | ≥1≥1C | ? |

11 | 0 | 5656C | 00 | 00 | 00 | ≥1≥1C | ? |

12 | 0 | 8888C | 586586C | 16321632C | 40604060C | ≥1≥1C | all |

13 | 0 | 140140C | 00 | 00 | 00 | ≥1≥1C | ? |

14 | 0 | 236236C | 00 | 00 | 00 | ≥1≥1C | ? |

15 | 0 | 402402C | 00 | 00 | 00 | ≥1≥1C | ? |

16 | 0 | 664664C | 66346634C | 2449624496C | 8855288552C | ≥1≥1C | all |

N>0 | x | all | ? | ? | ? | all |

Smallest common multiple (area 24):

Smallest known common multiple without holes (area 36):

Smallest known convex common multiple (area 48):

area | 12 | 24 | 36 | 48 |
---|---|---|---|---|

solutions | ? | ≥2 | ≥1 | ≥1 |

- Smallest rectangle and square found by Dmitry Grekov
- Solutions counted by Dmitry Grekov
- Smallest common multiple found by Jorge Mireles
- Holeless common multiple found by Dmitry Grekov
- Convex common multiple found by Dmitry Grekov