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PolyiamondA polyiamond is a counterpart to a polyomino where the polygon used as the building block is an equilateral triangle rather than a square. The word polyiamond is a back-formation from diamond, motivated by the fact that this word is often used to describe the shape of a pair of equilateral triangles placed base to base. Counting polyiamonds The basic combinatorial question is how many different polyiamonds with a given number of triangles exist. If mirror images are considered identical, the number of possible n-iamonds for n = 1, 2, 3, … is : - 1, 1, 1, 3, 4, 12, 24, 36, 66, 160, …
| the moniamond: | The moniamond | | the diamond: | The diamond | | the triamond: | The triamond |
the 3 tetriamonds: | The 3 tetriamonds |
the 4 pentiamonds: | The 4 pentiamonds |
Generalizations Like polyominoes, but unlike polyhexes, polyiamonds have a three dimensional counterparts. These are formed by aggregating tetrahedra.
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