  We introduce the concept of $\omega$-lattice, constructed from $\tau$
functions of Painlev\'e systems, on which quad-equations of ABS type appear. In
particular, we consider the $A_5^{(1)}$- and $A_6^{(1)}$-surface $q$-Painlev\'e
systems corresponding affine Weyl group symmetries are of $(A_2+A_1)^{(1)}$-
and $(A_1+A_1)^{(1)}$-types, respectively.
