Dust complexes form one of the Solar System components. The surface shape of a typical dust complex filled up by particles ejected from a celestial body is found within an analytical approach using reasonable assumptions (the main one is the smallness of perturbations). The parametric equations of the surface are obtained. The main properties of the surface are established and studied. Singular points are found and the topological type of the surface as a whole and in the vicinity of the conic point and the constriction is examined.