  In this paper, we give Thomae type formula for \KK surfaces $\cS$ given by
double covers of the projective plane branching along six lines. This formula
gives relations between theta constants on the bounded symmetric domain of type
$I_{22}$ and period integrals of $X$. Moreover, we express the period integrals
by using the hypergeometric function $F_S$ of four variables. As an application
of our main theorem, we define $\R^4$-valued sequences by mean iterations of
four terms, and express their common limits by the hypergeometric function
$F_S$.
