Polyiamonds

Polyiamonds are geometric figures formed by attaching equilateral triangles edgeto- edge in the plane without creating holes. Two sample polyiamonds are shown in Figures 1 and 2. Figure 1 shows a polyiamond obtained from a simple (non-self-intersecting) polygon by subdividing it into equilateral triangles, while Figure 2 has "internal" vertices. Our goal will be to show some properties of polyiamonds and indicate how much is still not known about these easy-to-describe and "experiment with" geometric objects.