Our acoustic to articulatory inversion method exploits an original codebook representing the articulatory space by hypercubes. The articulatory space is decomposed into regions where the articulatory-to-acoustic mapping is linear. Each region is represented by a hypercube. The inversion procedure retrieves articulatory vectors corresponding to an acoustic entry from the hypercube codebook. As the dimension of the articulatory space is greater than the dimension of the acoustic space, the corresponding null space is sampled by linear programming to retrieve all the possible solutions. A dynamic procedure is used to recover the best articulatory trajectory according to a minimum articulatory rate criterion. The addition of constraints allows the inversion process to be focused on realistic inverse articulatory trajectories.