Tiling Regular Hexagons with a Scaled Pentiamond and Hexiamond

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.

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