So, I've got a pretty interesting problem:

I was wondering how one would go about trying to generate every n-gon, or at least parametrize the space of a specific n-gon (say a hexagon) so it's easily spanned.

For instance, what are the best variables to define an n-gon such that one could easily cycle through them with a loop.

And then, how would one do this with polyhedra? One constraint is that all the shapes should have the same area/volume.

For some perspective, I'm currently running some physics computations that take in polyhedral meshes and output physical characteristics for each mesh, and we need to have a good way of cycling through the shapes.