Question

For metallic structures, does the packing efficiency (see sample exercise 12.1 in textbook) increase or decrease as the number of nearest neighbors (the coordination number) decreases?

Answer 1

Metallic solids or metallic structures experience metallic bonds which are the forces of attractions between the sea of electrons and the nucleus of the metallic atoms. They share a network of highly delocalized electrons.
I therefore think that the packing efficiency decreases as the number of nearest neighbors decreases.