Tile Idea

I have been interested for several years in the construction of 2d shapes by pasting equilateral triangles together by their edges.

- Two triangles pasted together at their edge create a rhombus.
- Three triangles can only be pasted together to create a single shape with two parallel sides and two non-parallel sides
- Four triangles can be pasted together in four ways to create four distinct shapes
- Five triangles can be pasted together in eight ways to create eight distinct shapes
- It gets tricky to count the combinations of six triangles but I remember diagramming between twenty and thirty a few years ago (lost the notebook!)

Anyway, I would love to design a combat maneuver game or possibly an exploration game based on a board with these unique shapes. Each shape would represent one piece of terrain. Long, thin shapes would represent roads or rivers that can be traversed quickly. Regular hexagons would represent plains. Smaller shapes (made of 2-4 triangles) would represent rugged terrain like forests and hills that take longer to traverse.