Large single crystals of the oxygen ion conductor BaBi 3 O 5.5 have been obtained, and its structure was investigated by singlecrystal X-ray di4raction (XRD) and neutron di4raction (ND), electron di4raction, and high-resolution electron microscopy (HREM). The basic three-dimensional structure was re5ned, using single crystal ND data, in space group Im3 m to a weighted R value of 5.3% for 17 unique re6ections, with Ba and Bi atoms statistically distributed on the 2(a) sites (0, 0, 0) and the O atoms on the 6(b) sites ( 12 , 0, 0) with a re5ned occupancy of 36(1)%. The re5ned thermal-displacement parameters for the O atoms are highly anisotropic, with U 11 ؍ U 22 ؍ 0.27(1) and U 33 ؍ 0.082(7) A s 2 . In addition, the structure is incommensurately modulated with the systematic absence conditions F1 1hklmnp2 2 ؍ 0 unless h ؉ k ؉ l ؍ 2j and m ؉ n ؉ p ؍ 2j, implying the six-dimensional superspace group P : Im3 m : Im3 m, with a ؍ 4.3798(2) A s and modulation vectors q 1 ؍ [ , 0, 0]*, q 2 ؍ [0, , 0]*, and q 3 ؍ [0, 0, ]* with ؍ 0.3835(1). The diffraction data and the HREM images indicate that the modulation is predominantly occuptional. The satellite re6ections have comparable intensities in powder XRD and ND patterns, indicating furthermore that the modulation originates from ordering of both O atoms/vacancies and metal atoms.