A simple way to find position is to use Convex Hull
Here i just use the 10 bigger (use the slider) faces to orient the object. One better way will use the center of gravity of the object, if it is on the triangular face, the object will be stable.
put object on plane.gh (12.3 KB)
And here a version with Center of Gravity. I had to add Dendro to have a valid volume has some ob closed brep doesn’t lead to closed mesh. But whatever I get an approximate closed volume that I use tp calculate CoG then I just take faces of the 3d convex hull that contains the CoG. I take the 1000 bigger faces. I obtain 8 stable positions.
A version with CoG, automatic flip and the bake from @magicteddy …
put object on plane with center of gravity and bake.gh (11.3 MB)