Whilst working on a Tangram problem, I came across the need to find the total number of convex shapes that can be produced from $16$ identical (isosceles) right angle triangles (since the Tangram can be subdivided in this way).
This should be something that can be computed by hand, but I am curious if there are any references that explore producing a general solution to this problem for $n$ (isosceles) right angle triangles and the total number of shapes that they can produce?
Is this something that has been explored before? And if so is there a result that I can reference?
To be make the problem rigorous:
- I am only allowing for rotation and translation of the triangles
- I would specifically be interested in the number of distinct convex polygons that can be made (however, if there are references on the instances where the shapes need not be distinct, then these would also be worth mentioning)
As mentioned in the comments, I have posted a request for a specific computational solution for $n=16$ on MSE. This question is fundamentally different, as I am looking for a reference request that generalizes the problem solution. Whereas, the other post does not request a solution that generalizes.