Three new salt inclusion compounds (CsX)Cu5O(2)(PO4)(2) (X = Cl, Br, I), phosphate analogues of the kagome mineral averievite, are reported. Their crystal structures are composed of trigonal networks of corner-sharing OCu4 anion centered tetrahedra, forming capped-kagome planes, which can also be regarded as two-dimensional slices along the [111] direction of a pyrochlore lattice. Magnetization and heat capacity measurements reveal strong geometric frustration of this network and complex magnetic behavior. X-ray and neutron diffraction studies show that all three compounds undergo a trigonal-to-monoclinic phase transition upon cooling, with a first-order phase transition seen in CsBr and CsI analogues. Along with the previously reported (CsCI)Cu502(VO4)2, these three new compounds belong to a large family of OCu4 based networks, which are a playground for studying frustrated quantum magnetism.