Math friends have helped me refine my question to: find the minimum-area regular n-gon circumscribing n points.
Conversation
After some more thought, I'm pretty sure this isn't actually what you want.
1
A minimum square bounding an isoceles triangle will suddenly flip 45 degrees as you increase the triangle width.
2
Replying to
Yeah, that's a good point. It helps (maybe?) that the number of sides is the number of points.
Your suggestion makes sense.