A novel fast Fourier transform-based ab inito docking algorithm called SAM is presented, for building perfectly symmetrical models of protein complexes with arbitrary point group symmetry. The basic approach uses a novel and very fast one-dimensional symmetry-constrained spherical polar Fourier search to assemble cyclic Cn systems from a given protein monomer. Structures with higher-order (Dn, T, O and I) point group symmetries may be built using a subsequent symmetry-constrained Fourier domain search to assemble trimeric sub-units. The results reported here show that the SAM algorithm can correctly assemble monomers of up to around 500 residues to produce a near-native complex structure with the given point group symmetry in 17 out of 18 test cases. The SAM program may be downloaded for academic use at http://sam.loria.fr/.