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: 4.

Smallest rectangle (2x3):

Smallest square (3x3):

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

1 | 0 | ||||

2 | 0 | 00 | |||

3 | 0 | 22P | 44P | ||

4 | 0 | 33P | 1010C | 3333C | |

5 | 0 | 77P | 2020C | 9292C | all |

6 | 0 | 1111C | 4242C | 267267C | all |

7 | 0 | 2020C | 8484C | 746746C | all |

8 | 0 | 3232C | 170170C | 21132113C | all |

9 | 0 | 5454C | 340340C | 59325932C | all |

10 | 0 | 8787C | 682682C | 1671516715C | all |

11 | 0 | 143143C | 13641364C | 4700247002C | all |

12 | 0 | 231231C | 27302730C | 132289132289C | all |

13 | 0 | 376376C | 54605460C | 372156372156C | all |

14 | 0 | 608608C | 1092210922C | ≥1≥1C | all |

15 | 0 | 986986C | 2184421844C | ≥1≥1C | all |

16 | 0 | 15951595C | 4369043690C | ≥1≥1C | all |

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

Smallest prime reptiles (1Ox3, 4Ox2):

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

O monomino | ? | ? | ?P | ?P |

O tetromino | ? | ?P | ?P | ?P |

Smallest common multiple (area 4):

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

solutions | 1P |