Polyiamond
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A polyiamond (also polyamond or simply iamond) is a polyform in which the base form is an equilateral triangle. 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 Template:OEIS:
- 1, 1, 1, 3, 4, 12, 24, 36, 66, 160, …
| the moniamond: |  |
| the diamond: |  |
| the triamond: |  |
| the 3 tetriamonds: |
Missing image Polyiamonds-4.png The 3 tetriamonds |
| the 4 pentiamonds: |
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Generalizations
Like polyominoes, but unlike polyhexes, polyiamonds have three-dimensional counterparts, formed by aggregating tetrahedra. However, polytetrahedra do not tile 3-space in the way polyiamonds can tile 2-space, so they are of little mathematical interest.
External links
- Polyiamond (http://mathworld.wolfram.com/Polyiamond.html) at MathWorld