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. The main issue is about how all the possible inverse solutions in a given hypercube could be found. 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. Indeed, the sampling of the null space is a crucial point because it directly controls the smoothness of articulatory trajectories recovered from the original signal. This approach permits more realistic articulatory trajectories to be obtained.