Tiling Regular Hexagons with a Scaled Pentiamond and Hexiamond
A pentiamond is a plane figure
formed by joining five equal equilateral triangles edge to edge.
There are 4 pentiamonds, independent of rotations and reflections:
A hexiamond is a plane figure
formed by joining six equal equilateral triangles edge to edge.
There are 12 hexiamonds, independent of rotations and reflections:
A scaled polyiamond is a polyiamond that may be scaled up
by an integer factor.
Here I show the fewest copies of two scalable hexiamonds
that can tile some regular hexagon.
If you find a smaller solution or solve an unsolved case,
please write.
See also
Table of Solutions
This table shows the fewest tiles known to be able to tile a regular hexagon.
| A | E | F | H | I | L | O | P | S | U | V | X |
I
| 10
| 8
| 7
| 13
| 7
| 8
| 7
| 6
| 13
| 8
| 10
| 10
|
J
| 10
| 9
| 10
| 10
| 10
| 10
| 7
| 8
| 18
| 10
| 10
| 18
|
Q
| 20
| 46
| 10
| 18
| 10
| 8
| 9
| 10
| 33
| 9
| 9
| 46
|
U
| 14
| —
| 14
| 27
| 10
| 44
| —
| 18
| —
| —
| 14
| —
|
6 Tiles
7 Tiles
8 Tiles
9 Tiles
10 Tiles
13 Tiles
14 Tiles
18 Tiles
27 Tiles
33 Tiles
44 Tiles
46 Tiles
Last revised 2025-03-31.
Back to Polyiamond and Polyming Tiling
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Polyform Curiosities
Col. George Sicherman
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