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Area: 12.

Perimeter: 18.

Size: 3x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 8.

Square order: 12.

Prime rectangles: ≥ 2.

Smallest rectangle (8x12):

Smallest square (12x12):

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 | 1-7 | 8 | 9-11 | 12 | 13-15 | 16 | 17-19 | 20 | 21-23 | 24 | N>0 |
---|---|---|---|---|---|---|---|---|---|---|---|

1-7 | 0 | ||||||||||

8 | 0 | 0 | |||||||||

9-11 | 0 | 0 | 0 | ||||||||

12 | 0 | 22P | 0 | 22P | |||||||

13-15 | 0 | 0 | 0 | 00 | 0 | ||||||

16 | 0 | 0 | 0 | 66C | 0 | 00 | |||||

17-19 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | ||||

20 | 0 | 0 | 0 | 1010C | 0 | 00 | 0 | 00 | |||

21-23 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | ||

24 | 0 | 44C | 0 | 2222C | 0 | 4040C | 0 | 302302C | 0 | 12601260C | |

25 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

26 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

27 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

28 | 0 | 0 | 0 | 4242C | 0 | 00 | 0 | 00 | 0 | 49584958C | ? |

29 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

30 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

31 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

32 | 0 | 0 | 0 | 8686C | 0 | 00 | 0 | 00 | 0 | 2484424844C | ? |

33 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

34 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

35 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

36 | 0 | 88C | 0 | 170170C | 0 | 272272C | 0 | 75787578C | 0 | 107350107350C | ? |

37 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

38 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

39 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

40 | 0 | 0 | 0 | 342342C | 0 | 00 | 0 | 00 | 0 | 477548477548C | ? |

41 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

42 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

43 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

44 | 0 | 0 | 0 | 682682C | 0 | 00 | 0 | 00 | 0 | 21901582190158C | ? |

45 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

46 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

47 | 0 | 0 | 0 | 00 | 0 | 00 | 0 | 00 | 0 | 00 | ? |

48 | 0 | 1616C | 0 | 13661366C | 0 | 18561856C | 0 | 194174194174C | 0 | 97364289736428C | ? |

N>0 | x | 12k | x | ? | x | ? | x | ? | x | ? |

Smallest prime reptile (12L1x12):

polyomino \ n² | 1² | 2² | 3² | 4² | 5² | 6² | 7² | 8² | 9² | 10² | 11² | 12² | 13² | 14² | 15² |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

L1 12-omino | ≥1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥4000000P | 0 | 0 | 0 |