This paper describes a process for applying Islamic geometric patterns (IGP) to the faces of polar zonohedra (PZ). First, a process for developing IGP that repeat on rhombic grids is presented. Then, PZ are defined and the formula for calculating the rhombic face angles is shown. Since the set of face angles for a given PZ is almost never identical to those of the rhombic grids for IGP, a system is presented for systematically identifying PZ and IGP whose rhombic angles are within a given threshold. IGP can then be applied to the faces of the identified PZ using small linear scaling factors — making distortions practically unnoticeable to the naked eye.