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 (1x3):

Smallest square (2x2):

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

1 | 00 | |||

2 | 00 | 44P | ||

3 | 22P | 1818C | 130130C | |

4 | 33P | 6565C | 811811C | all |

5 | 77P | 219219C | 50955095C | all |

6 | 1111C | 719719C | 3164531645C | all |

7 | 2020C | 23342334C | 196784196784C | all |

8 | 3232C | 75387538C | 12223961222396C | all |

9 | 5454C | 2428924289C | ≥4132045≥4132045C | all |

N>0 | all | all | all |

Smallest prime reptiles (1Ox2, 2Ix2):

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

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

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

Smallest common multiple (area 2):

area | 2 |
---|---|

solutions | 1P |