  We study $c$-preprojective roots for a Coxeter element $c$ of infinite
Coxeter group $W$. In particular, we consider the case when any positive root
is $c$-preprojective for some Coxeter element $c$. In this paper, by assuming
that the Coxeter graph of $W$ is cyclic, we establish that any positive root is
$c$-preprojective for some Coxeter element $c$ if and only if $W$ is an affine
Coxeter group.
