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Math friends have helped me refine my question to: find the minimum-area regular n-gon circumscribing n points.

maybe your English friends can translate for us plebeians? :P

Find the smallest polygon with n sides and equal angles which encloses a given set of n points.

(Equal angles doesn't imply regular.)

Replying to

Hey, you're right! Equal angles *and* equal lengths. Great diagram. :)