Crystal structures of the three polymorphs of Cu5(PO4)2(OH)4, namely pseudomalachite, ludjibaite, and reichenbachite, can be described as being composed of rods perpendicular to their crystal-chemical layering. Two different sorts of rods can be defined. Type 1 rods share rows of Cu coordination polyhedra, forming a series of slabs. Slab boundaries and slab interiors represent alternating geometric OD layers of two kinds, with layer symmetries close to P21/m and , which make up two different stacking schemes of geometric OD layers in the structures of ludjibaite and pseudomalachite. Such OD layers, however, are not developed in reichenbachite. Type 2 rods are defined as having columns of PO4 tetrahedra in the corners of the rods. In the Type 2 slabs composed of these rods, geometric Pg OD layers of glide-arrayed tetrahedra alternate with more complex OD layers; in ludjibaite this system of layers is oriented diagonally with respect to the Type 1 OD layer system. Two different OD stackings of Type 2 OD layers form the ludjibaite and reichenbachite structures but not that of pseudomalachite. Thus, ludjibaite might form disordered intergrowths with either of the other two members of the triplet but reichenbachite and pseudomalachite should not form oriented intergrowths. Current knowledge concerning formation of the three polymorphs is considered.