2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68442We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arbitrarily large families of walls in the wall space which pairwise cross.Updated to submitted versionGeometric TopologyGroup Theory20F65text