A polyiamond is a polyform consisting of a collection of equal-sized equilateral triangles arranged
with coincident sides. Polyiamonds are sometimes simply known as iamonds.
The top row of hexiamonds in the above figure are known as the bar , crook ,
crown , sphinx ,
snake , and yacht .
The bottom row of 6-polyiamonds are known as the chevron ,
signpost , lobster ,
hook , hexagon , and
butterfly .
The number of two-sided (i.e., can be picked up and flipped, so mirror image pieces are considered identical) polyiamonds made up of A000577 ). The number of one-sided polyiamonds
composed of A006534 ).
One of the 160 9-polyiamonds has a hole (Gardner 1984, p. 174).
The polyiamonds illustrated above are 2-trees .
The numbers of A070764 ;
Myers), the first few of which are illustrated above.
See also Polyabolo ,
Polyhex ,
Polyomino ,
Triangular
Snake Graph
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References Beeler, M. Item 112 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory,
Memo AIM-239, pp. 48-50, Feb. 1972. https://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112 . Clarke,
A. L. "Polyiamonds." http://www.recmath.com/PolyPages/PolyPages/Polyiamonds.htm . Gardner,
M. "Mathematical Games: On Polyiamonds: Shapes That Are Made Out of Equilateral
Triangles." Sci. Amer. 211 , 124-129, Dec. 1964. Gardner,
M. "Polyiamond." Ch. 18 in The
Sixth Book of Mathematical Games from Scientific American. Golomb, S. W. Polyominoes:
Puzzles, Patterns, Problems, and Packings, 2nd ed. Keller, M. "Counting Polyforms."
https://web.archive.org/web/20030803065351/http://members.aol.com/wgreview/polyenum.html . Myers,
J. "Polyomino Tiling." https://www.polyomino.org.uk/mathematics/polyform-tiling/ . O'Beirne,
T. H. "Pentominoes and Hexiamonds." New Scientist 12 ,
379-380, 1961. Pegg, E. Jr. "MathPuzzle: Iamonds." Jul. 30,
2012. https://www.mathpuzzle.com/iamond.htm . Reeve,
J. E. and Tyrrell, J. A. "Maestro Puzzles." Math. Gaz. 45 ,
97-99, 1961. Sloane, N. J. A. Sequences A000577 /M2374
and A006534 /M3287 in "The On-Line Encyclopedia
of Integer Sequences." Torbijn, I. P. J. "Polyiamonds."
J. Recr. Math. 2 , 216-227, 1969. Vichera, M. "Polyforms."
https://web.archive.org/web/20250831090700/https://www.vicher.cz/puzzle/polyforms.htm . von
Seggern, D. CRC
Standard Curves and Surfaces. Referenced on Wolfram|Alpha Polyiamond
Cite this as:
Weisstein, Eric W. "Polyiamond." From
MathWorld https://mathworld.wolfram.com/Polyiamond.html
Subject classifications
triangles are 1, 1, 1, 3, 4, 12, 24, 66, 160, 448, ... (OEIS
A000577). The number of one-sided polyiamonds
composed of 
triangles are 1, 1, 1, 4, 6, 19, 43, 121, ... (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.
