A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants to exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given.