Polyiamond

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 moniamond
the diamond: The diamond
the triamond: The triamond
 
the 3 tetriamonds:
Missing image
Polyiamonds-4.png
The 3 tetriamonds

 
the 4 pentiamonds:
The 4 pentiamonds

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
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