Hidden Symmetries in the Snub Dodecahedron

Among the 13 Archimedean polyhedra there are 6 polyhedra with icosahedral symmetry. Of these 6 polyhedra the snub dodecahedron is exceptional, as it has no reflection symmetries. We are going to show that the intersection points of certain couples of edges of the snub dodecahedron define a polyhedron with reflection symmetries.