The crystal structure of baliczunicite, Bi₂O(SO₄)₂, a new mineral species from the La Fossa crater of Vulcano (Aeolian Islands, Italy), was solved from single-crystal X-ray diffraction data and refined to R = 0.0507. The structure is triclinic, space group P1¯, with a = 6.7386(3), b = 11.1844(5), c = 14.1754(7)Å , α = 80.082(2)^o, β = 88.462(2)º, γ = 89.517(2)º, V = 1052.01(8)ų and Z = 6. The crystal structure consists of six independent Bi sites, six S sites and 27 O sites of which three are oxo oxygen atoms not bonded to sulfur. Bismuth and S atoms are arranged close to a eutectic pattern parallel to the (100) plane. The planes are stacked atom on atom such that Bi always overlays S and vice versa. This structural feature is shared with the known structure of the high-temperature polymorph of the same compound, stable at T >535^oC. However, the sequences of Bi and S atoms in the two structures are different and so are the arrangements of oxygen atoms. Characteristic building blocks in the structure of balic´zˇunic´ite are clusters of five Bi atoms which form nearly planar trapezoidal Bi₅ groups with oxo oxygens located in the centres of the three Bi₃ triangles, which form the trapezoids. The trapezoidal Bi₅O₃⁹⁺ ions are joined along [100] with SO₄^2- groups by means of strong bismuth-sulphate oxygen bonds, forming infinite [100] rods with composition Bi₅O₃(SO₄)^5-. One sixth of the Bi atoms do not participate in trapezoids, but form, with additional SO₄^2- groups, rows of composition BiSO₄⁺, also parallel to [100]. [Bi₅O₃(SO₄)_5^-] rods form infinite layers parallel to (010) with [BiSO₄⁺] rows located on the irregular surface of contact between adjacent layers. Bi atoms occur in four different coordination types, all showing the stereochemical influence of the Bi³⁺ lone electron pair. In this respect the crystal structure of balic´zˇunic´ite shows greater variability than its high-temperature polymorph which has only two types of the Bi coordination spheres present in balic´zˇunic´ite.