  In this paper we develop in detail the geometric constructions that lead to
many uniqueness results for the determination of polyhedral sets, typically
scatterers, by a finite minimal number of measurements. We highlight how unique
continuation and a suitable reflection principle are enough to proceed with the
constructions, without any other assumption on the underlying partial
differential equation or the boundary condition. We also aim to keep the
geometric constructions and their proofs as simple as possible.
  To illustrate the applicability of this theory, we show how several
uniqueness results present in the literature immediately follow from our
arguments. Indeed we believe that this theory may serve as a roadmap for
establishing similar uniqueness results for other partial differential
equations or boundary conditions.
