There are a number of tilings of various shapes by all the 12 order 
polyiamonds, summarized in the following table. Several
of these (starred in the table below) are also illustrated above (Beeler 1972). Beeler's
numbers for the side 6 parallelogram of base 6 and side 4 trapezoid (156 and 76,
respectively), differ from those quoted in Gardner (1984, p. 182) of 155 and
74, respectively.
| size | solutions |
side 9 
with inverted side 3 
hole | 0 |
| side 6 trapezoid with bases 3 and 9 | 0 |
| two side 6 triangles | 0 |
 rhomboid | 0 |
 rhomboid* | 37 |
| side 4 trapezoid with bases 7 and 11* | 76 |
| side 6 parallelogram of base 6* | 156 |
| triangle of side 9 with 1, 2, 2 corners removed* | 5885 |
| trefoil* | several |
The following table gives the number of solutions to various hexiamond tilings using fewer than 12 pieces. Those indicated with asterisks (*) have a solution illustrated above.
| Size | Pieces | Solutions |
| 2-hexagon |  | |
| 3-hexagon* | 9 |  |
equilateral  | 0 | |
| hexagonal ring | 0 | |
| 6-point star* | 8 | 1 |
| triangular ring | 0 | |
 rhomboid | 0 | |
 rhomboid* | 4 | 1 |
 rhomboid | 3 | 0 |
 rhomboid | 4 | many |
 rhomboid | 5 | many |
 rhomboid | 6 | many |
 rhomboid | 7 | many |
 rhomboid | 8 | many |
 rhomboid | 9 | many |
 rhomboid | 10 | many |
 rhomboid* | 11 | 24 |
 rhomboid | 8 |  |
 rhomboid | 10 | many |
