  In this paper we study the right-angled Coxeter groups that acts
geometrically on the Salvetti complex of a certain right-angled Artin group,
which we refer to as Croke-Kleiner spaces. We prove that any right-angled
Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with
$\pi/2$ angles between reflecting axes, while the quasi-isometric right-angled
Artin group can act with angles that are any real number in the range $(0,
\pi/2]$. The contrast between the two examples shows that in this case a
right-angled Coxeter group is geometrically more "rigid" than its quasi
isometric counterpart.
