The crystal structure of the stable crystalline form of syndiotactic polypropylene (s-PP) may be taken, only as a first approximation, as body-centered orthorhombic and described in the space group Ibca (in which the chains maintain their full, ideal 2(1)22 symmetry). Indeed, the splitting of the resonance of the methyl carbons, observed in the solid state C-13 NMR spectra of annealed samples of s-PP in this crystalline form, reported by Sozzani et al., and the observation by Lovinger and Lotz of a 011 reflection in the electron diffraction spectra of single crystals of s-PP grown at high temperature may be taken as indications of a symmetry lower than that of Ibca for the limit, fully ordered structure. We have refined, through the Rietveld method, various structural models for which right- and left-handed helices are repeated along the a and b axes as in the space group Ibca, but the full 2(1)22 chain symmetry is not maintained. We started with the model of higher symmetry (space group Ibca) and then space groups of lower symmetry were analyzed. In the refined models, while the unit cell constants are almost unvaried (a = 14.31 +/- 0.07 Angstrom, b = 11.15 +/- 0.02 Angstrom, c = 7.5 +/- 0.1, gamma = 90.3 +/- 1.5 degrees) and, thus, the positions of the chain axes are practically the same as in the Ibca space group, the lattice is primitive (P), instead of body-centered (I), and the chains are slightly rotated (+/-5 degrees) around the chain axis and significantly shifted (approximate to 0.07c) along the chain axis with respect to the previously assumed position, having 2(1)22 crystallographic symmetry. This results in a noncrystallographic equivalence of the methyl groups, which have then slightly different packing environments. The space group is P2(1)/a.