Apatites commonly adopt P6(3)/m hexagonal symmetry. More rarely, monoclinic chemical analogues have been recognized, including the biologically significant hydroxyapatite, Ca(10)(PO(4))(6)(OH)(2), but the driving force towards lower symmetry has not been systematically examined. A combination of diffraction observations and ab initio calculations for Ca(10)(AsO(4))(6)F(2) and Ca(10)(VO(4))(6)F(2) show these materials are triclinic P\bar 1 apatites in which the AsO(4) and VO(4) tetrahedra tilt to relieve stress at the metal and metalloid sites to yield reasonable bond-valence sums. An analysis of the triclinic non-stoichiometric apatites La(10 - x)(GeO(4))(6)O(3 - 1.5x) and Ca(10)(PO(4))(6)(OH)(2 - x)O(x/2) confirms this scheme of tetrahedral rotations, while Cd(10)(PO(4))(6)F(2) and Ca(10)(CrO(4))(6)F(2) are predicted to be isostructural. These distortions are in contrast to the better known P112(1)/b monoclinic dimorphs of chloroapatite and hydroxyapatite, where the impetus for symmetry reduction is ordered anion (OH(-) and Cl(-)) displacements which are necessary to obtain acceptable bond lengths. These results are important for designing apatites with specific structural and crystal-chemical characteristics.