## Hexiamonds

Polyamonds are obtained by joining equilateral triangles. There is only one mono-, dia- and triamond, 3 tetriamonds, 4 pentiamonds, 12 hexiamonds and 24 hetiamonds. With 12 tiles the Hexiamonds are best suited for a laying game.

## Solubility of Hexiamond Figures

Each figure and each Hexiamond token consists of 2 different “types” of triangles: Triangles with point up and triangles with point down. In 10 of the 12 hexiamonds, 3 triangles point upwards and 3 point downwards. For the other two hexiamonds shown below, the ratio of the two types of triangles is 4 to 2.

If you add the triangles with point upwards and the triangles with point downwards for a figure consisting of all 12 hexiamonds, the difference between the two sums may only be 0, 4 or -4. Otherwise no solution can exist. In my solution program Hexia I called this value parity.

## Auf dieser Webseite finden Sie

- Templates for making a Hexiamond game from cardboard
- Hexiamond figure overview
- 3d print templates
- solver for hexiamond figures

## Links