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A geometric study of two 4-dimensional mappings is given. By the resolutionof indeterminacy they are lifted to pseudo-automorphisms of rational varietiesobtained from $({\mathbb P}^1)^4$ by blowing-up along sixteen 2-dimensionalsubvarieties. The symmetry groups, the invariants and the degree growth ratesare computed from the linearisation on the corresponding N\'eron-Severibilattices. It turns out that the deautonomised version of one of the mappingsis a B\"acklund transformation of a direct product of the fourth Painlev\'eequation which has $A_2^{(1)}+A_2^{(1)}$ type affine Weyl group symmetry, whilethat of the other mapping is of Noumi-Yamada's $A_5^{(1)}$ Painlev\'e equation.

Space of initial conditions and geometry of two 4-dimensional discrete Painlev\'e equations