The equivalence between Aperture Field Integration Method (AFIM) and Physical Optical (PO) is discussed for polyhedron surfaces in this paper. The necessary conditions for the equivalence are summarized which demand complete equivalent surface currents and complete apertures. The importance of the exact expressions for both incident and reflected fields in constructing equivalent surface currents is emphasized and demonstrated numerically. The fields from reflected components on additional surface which lies on the Geometrical Optics (GO) reflection boundary are evaluated asymptotically. The analytical expression enhances the computational efficiency of the complete AFIM. The equivalent edge currents (EECs) for AFIM (AFIMEECs) are used to extract the mechanism of this equivalence between AFIM and PO.