Actions of right-angled Coxeter groups on the Croke-Kleiner spaces

It is an open question whether right-angled Coxeter groups have unique group-equivariant visual boundaries. In Croke and Kleiner (Topology 39(3):549-556, 2000. doi:10.1016/S0040-9383(99)00016-6), presented a right-angled Artin group with more than one visual boundary. In this paper we examine the space constructed by Croke and Kleiner and present a right-angled Coxeter group that is quasi-isometric to this space. Then we change the geometric parameters of this space to show that the proposed right-angled Coxeter group has non-unique equivariant visual boundaries, hence answer the open question negatively.