The worst imperfection advanced for simple critical points in Chap. 4 is extended in this chapter to systems with dihedral group symmetry based on the group-theoretic bifurcation theory in Chap. 8 and its application to the dihedral group Dn in Chap. 9. This group expresses the symmetry of domes and shells that are highly sensitive to imperfections. In their design, it is important to capture the “worst imperfection” that reduces the critical load most rapidly. This chapter is a prerequisite for Chap. 11.