Certain complex structures are logically regarded as intergrowths of chemically or topologically discrete modules. When the proportions of these components vary systematically a polysomatic series is created, whose construction provides a basis for understanding defects, symmetry alternation and trends in physical properties. Here, we describe the polysomatic family A(5N)B(3N)O(9N + 6)X(Ndelta) (2 < or = N < or = infinity) that is built by condensing N apatite modules (A(5)B(3)O(18)X(delta)) in configurations to create B(n)O(3n + 1) (1 < or = n < or = infinity) tetrahedral chains. Hydroxyapatite [Ca(10)(PO(4))(6)(OH)(2)] typifies a widely studied polysome where N = 2 and the tetrahedra are isolated in A(10)(BO(4))(6)X(2) compounds, but N = 3 A(15)(B(2)O(7))(3)(BO(4))(3)X(3) (ganomalite) and N = 4 A(20)(B(2)O(7))(6)X(4) (nasonite) are also known, with the X site untenanted or partially occupied as required for charge balance. The apatite modules, while topologically identical, are often compositionally or symmetrically distinct, and an infinite number of polysomes is feasible, generally with the restriction being that an A:B = 5:3 cation ratio be maintained. The end-members are the N = 2 polysome with all tetrahedra separated, and N = infinity, in which the hypothetical compound A(5)B(3)O(9)X contains infinite, corner-connected tetrahedral strings. The principal characteristics of a polysome are summarized using the nomenclature apatite-(A B X)-NS, where A/B/X are the most abundant species in these sites, N is the number of modules in the crystallographic repeat, and S is the symmetry symbol (usually H, T, M or A). This article examines the state-of-the-art in polysomatic apatite synthesis and crystallochemical design. It also presents X-ray and neutron powder diffraction investigations for several polysome chemical series and examines the prevalence of stacking disorder by electron microscopy. These insights into the structure-building principles of apatite polysomes will guide their development as functional materials.