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Hexiamond Tiling


PolyiamondTiling

There are a number of tilings of various shapes by all the 12 order n=6 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.

sizesolutions
side 9 Delta with inverted side 3 Delta hole0
side 6 trapezoid with bases 3 and 90
two side 6 triangles0
3×12 rhomboid0
4×9 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
HexiamondTiling2

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.

SizePiecesSolutions
2-hexagon>=1
3-hexagon*9>=15
equilateral Delta0
hexagonal ring0
6-point star*81
triangular ring0
2×3 rhomboid0
2×6 rhomboid*41
3×3 rhomboid30
3×4 rhomboid4many
3×5 rhomboid5many
3×6 rhomboid6many
3×7 rhomboid7many
3×8 rhomboid8many
3×9 rhomboid9many
3×10 rhomboid10many
3×11 rhomboid*1124
4×6 rhomboid8>=1
5×6 rhomboid10many

See also

Heptiamond Tiling, Hexiamond, Octiamond Tiling, Pentiamond Tiling, Polyhex Tiling, Polyiamond, Polyomino Tiling

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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. http://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112.Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 176-181, 1984.Vichera, M. "Polyiamonds." http://www.vicher.cz/puzzle/polyform/iamond/iamonds.htm.

Referenced on Wolfram|Alpha

Hexiamond Tiling

Cite this as:

Weisstein, Eric W. "Hexiamond Tiling." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HexiamondTiling.html

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