The method for constructing 3D fractals of stars with icosahedral symmetry is proposed. A great stellated dodecahedron (I) and a small stellated dodecahedron (D) were selected as building elements. The faces of the polyhedra are equal in size. The initial polyhedron (I or D) is replicated and the copies are placed so that its centres coincide with the vertices of the star (I or D), which is not displayed. This star is called by the author the generalized star, its size is τ N times the size of the initial star, where τ = (1 + 50.5)/2 ≈ 1.618 is the golden mean, N is a non-negative integer. At each next step of the construction, the previous prefractal is replicated and the copies are placed so that its centres coincide with the vertices of the generalized star. The series of integers N forms a non-decreasing sequence. The types of generalized stars (I or D) can vary at every step. Coinciding points are counted once. Initial polyhedra can touch each other by vertices, overlap each other or stand separately. Like in the Penrose 3D tiling, all the vertices of these fractals belong to the symmetric projection of a simple 6D cubic lattice onto a 3D space.