The fourth lifting method enables to exploit symmetry relations. The idea is to classify points into orbits and to give every orbit the same height. The induced subdivision is symmetric and only the generating solutions have to be computed.
Just as with symmetric set structure analysis, it is hard to guarantee the same level of robustness, because deficiency is often induced by symmetry. The range of applications is though enlarged significantly, when compared to symmetric linear-product systems. The current implementation includes an exhaustive procedure to check whether a proper symmetric subdivision can be constructed.