Final answer:
The statement in question is false as lattice energy plays a pivotal role in the stability of ionic structures, with factors such as the size of the ions and charge states (divalent versus monovalent) influencing stability rather than the presence of common faces or edges in coordination polyhedra.
Step-by-step explanation:
The statement that the existence of edges, and particularly of faces, common to coordination polyhedra decreases the stability of ionic structures is false. In fact, the stability of ionic structures is greatly influenced by lattice energy, which is usually the most important factor determining the stability of an ionic compound.
Lattice energy is affected by the sizes of the ions involved; as the ionic radii increase, the lattice energies decrease. Additionally, solids comprised of divalent ions usually have much larger lattice energies compared to those with monovalent ions, due to the greater charge leading to stronger electrostatic attractions in the lattice.
Many ionic structures, such as face-centered cubic lattices, are energetically stable. It is when the inserted atoms are too large and disrupt the close-packed arrangement that the lattice can lose stability. Therefore, coordination polyhedra with common faces or edges do not inherently decrease stability; rather, the overall size of the ions and their ability to fit into an efficient packing structure without causing distortion are key factors determining the stability of ionic solids.