Here I show the fewest number of copies of a pentiamond and a hexiamond that can tile some pentagonal polyiamond, letting the tiles be scaled up in size.

Empty cells in the table indicate that no such tiling exists. If you find tilings with fewer tiles than those shown, please write.

5I+6A : 3 | 5J+6A : 6 | 5Q+6A : 3 | 5U+6A : 2 |
---|---|---|---|

5I+6E : 6 | 5J+6E : 6 | 5Q+6E : 27 | 5U+6E : 0 |

5I+6F : 3 | 5J+6F : 5 | 5Q+6F : 3 | 5U+6F : 2 |

5I+6H : 6 | 5J+6H : 5 | 5Q+6H : 15 | 5U+6H : 0 |

5I+6I : 2 | 5J+6I : 4 | 5Q+6I : 2 | 5U+6I : 4 |

5I+6L : 2 | 5J+6L : 4 | 5Q+6L : 5 | 5U+6L : 0 |

5I+6O : 5 | 5J+6O : 10 | 5Q+6O : 2 | 5U+6O : 0 |

5I+6P : 2 | 5J+6P : 2 | 5Q+6P : 3 | 5U+6P : 3 |

5I+6S : 7 | 5J+6S : 10 | 5Q+6S : 25 | 5U+6S : 0 |

5I+6U : 5 | 5J+6U : 2 | 5Q+6U : 2 | 5U+6U : 0 |

5I+6V : 3 | 5J+6V : 2 | 5Q+6V : 3 | 5U+6V : 7 |

5I+6X : 3 | 5J+6X : 6 | 5Q+6X : 27 | 5U+6X : 0 |

*Last revised 2024-08-06.*

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Col. George Sicherman [ HOME | MAIL ]