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