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Area: 6.

Size: 2x4.

Holes: 0.

Order: 2.

Square order: 6.

Odd order: 11.

Prime rectangles: 5.

Some facts:

- It is smallest polyomino which have two smallest rectangles

Smallest rectangles (2x6, 3x4):

Smallest square (6x6):

Smallest odd rectangle (6x11):

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

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

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

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

4 | 0 | 0 | 22P | 0 | |||||||||

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

6 | 0 | 22P | 0 | 88C | 00 | 4848C | |||||||

7 | 0 | 0 | 0 | 0 | 0 | 00 | 0 | ||||||

8 | 0 | 0 | 44C | 0 | 0 | 202202C | 0 | 0 | |||||

9 | 0 | 0 | 0 | 3232C | 0 | 00 | 0 | 24442444C | 0 | ||||

10 | 0 | 0 | 0 | 0 | 0 | 880880C | 0 | 0 | 37603760P | 0 | |||

11 | 0 | 0 | 0 | 0 | 0 | 3232P | 0 | 0 | 0 | 0 | 0 | ||

12 | 0 | 44C | 88C | 114114C | 7272C | 44104410C | 35123512C | 8592685926C | ≥1000≥1000C | ≥1000≥1000C | ≥1000≥1000C | ≥1000≥1000C | |

13 | 0 | 0 | 0 | 0 | 0 | 192192C | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | 6k |

14 | 0 | 0 | 0 | 0 | 0 | 1992019920C | 0 | 0 | ≥1000≥1000C | 0 | 0 | ≥1000≥1000C | 3k |

15 | 0 | 0 | 0 | 456456C | 0 | 10241024C | 0 | 13799261379926C | 0 | ≥1000≥1000C | 0 | ≥1000≥1000C | 2k |

16 | 0 | 0 | 1616C | 0 | 0 | 9128291282C | 0 | 0 | ≥1000≥1000C | 0 | 0 | ≥1000≥1000C | 3k |

17 | 0 | 0 | 0 | 0 | 0 | 72967296C | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | 6k |

18 | 0 | 88C | 0 | 17121712C | 384384P | 431496431496C | 131232131232C | ≥1≥1C | ≥1000≥1000C | ≥1000≥1000C | ≥1000≥1000C | ≥1000≥1000C | all |

19 | 0 | 0 | 0 | 0 | 0 | 3968039680C | 0 | 0 | 0 | 0 | 0 | ≥1000≥1000C | 6k |

20 | 0 | 0 | 3232C | 0 | 0 | 19895701989570C | 0 | 0 | ≥1000≥1000C | 0 | 0 | ≥1000≥1000C | 3k |

N>0 | x | 6k | 4k | 3k | 6k | all | 6k | 3k | 2k | 3k | 6k | all |

Smallest prime reptile (6Px2):

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

P hexomino | 1 | 1P | 4P | 13337C | 3920564P | ≥12230590464C |