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Area: 7.

Perimeter: 16.

Size: 2x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: 27.

Prime rectangles: 2.

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest odd rectangle (9x21):

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 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | N>0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | ||||||||||||||

2 | 0 | 0 | |||||||||||||

3 | 0 | 0 | 0 | ||||||||||||

4 | 0 | 0 | 0 | 0 | |||||||||||

5 | 0 | 0 | 0 | 0 | 0 | ||||||||||

6 | 0 | 0 | 0 | 0 | 0 | 0 | |||||||||

7 | 0 | 22P | 0 | 44C | 0 | 88C | 0 | ||||||||

8 | 0 | 0 | 0 | 0 | 0 | 0 | 1616C | 0 | |||||||

9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||

10 | 0 | 0 | 0 | 0 | 0 | 0 | 3232C | 0 | 0 | 0 | |||||

11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||

12 | 0 | 0 | 0 | 0 | 0 | 0 | 6464C | 0 | 0 | 0 | 0 | 0 | |||

13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||

14 | 0 | 44C | 0 | 1616C | 0 | 6464C | 128128C | 264264C | 15361536C | 10961096C | 1075210752C | 45624562C | ≥1000≥1000C | ≥1000≥1000C | |

15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

16 | 0 | 0 | 0 | 0 | 0 | 0 | 256256C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

18 | 0 | 0 | 0 | 0 | 0 | 0 | 512512C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

20 | 0 | 0 | 0 | 0 | 0 | 0 | 10241024C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

21 | 0 | 88C | 0 | 6464C | 0 | 512512C | 0 | 43524352C | 512512P | 3788837888C | 92169216C | 333824333824C | ≥1000≥1000C | ≥1000≥1000C | ? |

22 | 0 | 0 | 0 | 0 | 0 | 0 | 20482048C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

24 | 0 | 0 | 0 | 0 | 0 | 0 | 40964096C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

26 | 0 | 0 | 0 | 0 | 0 | 0 | 81928192C | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | ? |

28 | 0 | 1616C | 0 | 256256C | 0 | 40964096C | 1638416384C | 7188871888C | 26296962629696C | 13153921315392C | 124333056124333056C | ≥143000≥143000C | ≥1000≥1000C | ≥1000≥1000C | ? |

N>0 | x | 7k | x | 7k | x | 7k | 2k | 7k | 7k | 7k | 7k | 7k | 7k | all |

Smallest prime reptile (7L1x6):

polyomino \ n² | 1² | 2² | 3² | 4² | 5² | 6² | 7² | 8² |
---|---|---|---|---|---|---|---|---|

L1 heptomino | 1 | 0 | 0 | 0 | 0 | 12288P | 1572864P | ≥1100000P |