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A generic finite presentation defines a word hyperbolic group whose boundaryis homeomorphic to the Menger curve. In this article, we produce the firstknown examples of non-hyperbolic $CAT(0)$ groups whose visual boundary ishomeomorphic to the Menger curve. The examples in question are the Coxetergroups whose nerve is a complete graph on $n$ vertices for $n\geq 5$. Theconstruction depends on a slight extension of Sierpi\'nski's theorem onembedding $1$--dimensional planar compacta into the Sierpi\'nski carpet. Seethe appendix for a brief erratum.

Nonhyperbolic Coxeter groups with Menger curve boundary (with erratum)