  In this paper we discuss the dynamics as well as the structure of the
parameter space of the one-parameter family of rational maps $\ds
f_t(z)=-\frac{t}{4}\frac{(z^{2}-2)^{2}}{z^{2}-1}$ with free critical orbit
$\pm\sqrt{2}\xrightarrow{(2)}0\xrightarrow{(4)}t\xrightarrow{(1)}...$. In
particular it is shown that for any escape parameter $t$ the boundary of the
basin at infinity $\A_t$ is either a Cantor set, a curve with infinitely many
complementary components, or else a Jordan curve. In the latter case the Julia
set is a Sierpi\'nski curve.
