We haven't determined whether every finite set of geometric points can always be enclosed within a uniquely defined smallest possible shape of a specific type.
open
Global / Unspecified, Global
WS01348
Enclosing shape problems, like finding the smallest circle or polygon containing a set of points, are solved for many specific shape types, but a fully general theory covering every possible enclosing shape remains incomplete. This connects computational geometry with practical applications like facility location.