  We present a detailed study of the ground state phase diagram of the
classical frustrated Heisenberg model on the face-centered-cubic lattice. By
considering exchange interactions up till third nearest neighbors, we find
commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which
include noncoplanar and chiral spin structures. We reveal the presence of
subextensively degenerate manifolds that appear at triple points and certain
phase boundaries in the phase diagram. Within these manifolds, the spin
Hamiltonian can be recast as a complete square of spins on finite motifs,
permitting us to identify families of exact ground state spin configurations in
real space -- these include randomly stacked ferro- or antiferromagnetically
ordered planes and interacting ferromagnetic chains, among others. Finally, we
critically investigate the ramifications of our findings on the example of the
Ising model, where we exactly enumerate all the states numerically for finite
clusters.
