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 | 77P | 2828P | ||

5 | 0 | 0 | 160160P | 0 | |

6 | 0 | 7171P | 696696C | 75017501P | ? |

7 | 0 | 0 | 29452945C | 0 | ? |

8 | 0 | 539539C | 1203512035C | 284470284470C | ? |

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

Smallest prime reptiles (2Ix3, 4Tx3):

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

I domino | 0 | 0 | 71P |

T tetromino | 0 | 0 | 22392P |

Smallest common multiple (area 8):

area | 4 | 8 |
---|---|---|

solutions | 0 | ≥2P |