Tiling Pentagons with a Scaled Pentiamond and Hexiamond
A pentiamond is a plane figure formed by joining 5 equilateral
triangles edge to edge.
A hexiamond is a plane figure formed by joining 6 equilateral
triangles edge to edge.
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.
Back to Polyiamond and Polyming Tiling
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Polyform Curiosities
Col. George Sicherman
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