  For Tur\'an's (3, 4)-conjecture, in the case of n = 3k+1 vertices,
(.5)6^{k-1} non-isomorphic complexes are constructed that attain the
conjecture. In the case of n = 3k+2 vertices, 6^{k-1} non-isomorphic complexes
are constructed that attain the conjecture.
