  A big open problem in $AdS_3 \times S^3 \times T^4$ holographic duality is to
compute the CFT data of the dual theory. In this direction recently it was
introduced the hexagonalization framework in the $AdS_3$ context. It allows the
computation of the structure constants of the CFT$_2$ dual in the planar limit
non-perturbatively, however in this proposal it was introduced only the
asymptotic part of the hexagon valid for correlators with asymptotically large
bridge lengths. In this work we complete this picture by computing the so
called mirror corrections that allow to describe structure constants for finite
bridge lengths and as a byproduct we also prove that the half-BPS operators in
the theory do not receive these corrections. We end up by giving the first
steps on using hexagonalization to compute $n$-point functions in the $AdS_3
\times S^3 \times T^4$ holographic duality.
