A polyiamond is a polyform consisting of a finite nonempty edge-connected union of congruentequilateral
triangles from the regular triangular tessellation.
Its cells are joined along complete sides, and holes are allowed. Polyiamonds are
sometimes simply known as iamonds.
Free (or two-sided) polyiamonds identify translations, rotations, and reflections.
The numbers composed of ,
2, ... triangles are 1, 1, 1, 3, 4, 12, 24, 66, 160,
448, ... (OEIS A000577). One-sided polyiamonds
identify translations and rotations
but do not allow reflections. Their numbers for , 2, ... are 1, 1, 1, 4, 6, 19, 43,
120, ... (OEIS A006534). One of the 160 9-polyiamonds
has a hole (Gardner 1984, p. 174).
The numbers of -polyiamonds
with holes for ,
10, 11, ... are 1, 4, 25, 108, 450, ... (OEIS A070764;
Myers), the first few of which are illustrated above.
,
2, ... triangles are 1, 1, 1, 3, 4, 12, 24, 66, 160,
448, ... (OEIS A000577). One-sided polyiamonds
identify translations and rotations
but do not allow reflections. Their numbers for 
, 2, ... are 1, 1, 1, 4, 6, 19, 43,
120, ... (OEIS A006534). One of the 160 9-polyiamonds
has a hole (Gardner 1984, p. 174).
-polyiamonds
with holes for 
,
10, 11, ... are 1, 4, 25, 108, 450, ... (OEIS A070764;
Myers), the first few of which are illustrated above.
Rangel-Mondragón, J. "Polyominoes and Related Families."
Mathematica J. 9, 609-640, 2005.