I am working on a Tangram problem which makes use of the techniques used in the proof of the number of convex polygons that can be made from the pieces.
Here, 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 feels like something that can be computed by hand, but I am curious if there is a computational (or otherwise rigorous) solution as a better way to work this out?
Is this something that has been explored before?
I am only allowing for rotation and translation of the triangles
I am more 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 reference request on math overflow for the general case for an arbitrary choice of $n$. This question is fundamentally different, as I am looking for a computational solution that specifically deals with the case of $n=16$ that does not necessarily generalise.