A method based on the physical space Patterson (pair correlation) function is derived which allows the determination of the correct $n$-$D$ Bravais lattice of quasicrystals. [Hereafter, we will abbreviate $n$-$D$ for $n$ dimensional. We will also call perpendicular space the $(n\ensuremath{-}3)$-$D$ orthogonal space that is added to physical 3D space to form the $n$-$D$ embedding space.] The optimum unit cell can be chosen and therefore the proper indexing of the diffraction pattern. The size of the integrated maxima of the Patterson function depends on their multiplicity and on their perpendicular space component. Lifting the positions of these maxima into $n$-$D$ space allows the set of ``quasilattice'' vectors to be distinguished from the set of decoration vectors. This procedure leads to a unique $n$-$D$ lattice. Taking advantage of scaling symmetries, the best choice of the $n$-$D$ unit cell can be found. A detailed analysis of the decoration vectors reveals all possible positions of the hyperatoms therein. This powerful technique is illustrated on simulated data of a decorated Fibonacci chain and on experimental data of decagonal ${\mathrm{Al}}_{70.5}{\mathrm{Mn}}_{16.5}{\mathrm{Pd}}_{13}$ quasicrystals.