The incommensurately modulated structure of K(3)In(PO(4))(2) has been solved and refined. The origin of the modulation relates to the ordering of K cations within the hexagonal close packing of the PO(4) anions. The driving forces for the modulation of the other cations are In-P and K-P interactions. The modulation of O atoms of rigid PO(4) units follows the cations in order to stabilize the InO(6) octahedron. It is shown that the previously published three-dimensional structure refined from powder diffraction data obtained at room temperature is an average structure. Therefore the incommensurately modulated phase of K(3)In(PO(4))(2) is the only one that has been unequivocally identified at room temperature. The origin of the modulation is discussed in comparison with the structures of Na(3)InP(2), alpha- and beta-Na(3)In(PO(4))(2), Na(3)Fe(PO(4))(2) and Rb(3)In(PO(4))(2).