  We numerically investigate the six-species predator-prey game in complex
networks as well as in $d$-dimensional hypercubic lattices with $d=1,2,..., 6$.
The interaction topology of the six species contains two loops, each of which
is composed of cyclically predating three species. As the mutation rate $P$ is
lowered below the well-defined phase transition point, the $Z_2$ symmetry
related with the interchange of the two loops is spontaneously broken, and it
has been known that the system develops the defensive alliance in which three
cyclically predating species defend each other against the invasion of other
species. In the small-world network structure characterized by the rewiring
probability $\alpha$, the phase diagram shows the reentrant behavior as
$\alpha$ is varied, indicating a twofold role of the shortcuts. In
$d$-dimensional regular hypercubic lattices, the system also exhibits the
reentrant phase transition as $d$ is increased. We identify universality class
of the phase transition and discuss the proper mean-field limit of the system.
