Final answer:
Cations with large valence and small coordination numbers in crystal structures typically do not share polyhedral elements due to their smaller size, influencing the crystal's properties and stability.
Step-by-step explanation:
When examining crystal structures, it is noted that cations with a large valence and a small coordination number tend not to share polyhedral elements. This is because large valence cations are typically smaller in size, which allows them to fit into the crystalline structure without the need to share their environment space. Conversely, smaller valence cations are larger and cannot as easily accommodate within the lattice without sharing. Ionic crystals, such as those formed from Group 1 or Group 2 metals with Group 16 or 17 nonmetals, display these properties. The structure of the crystal affects properties such as melting point, brittleness, and electrical conductivity.
For example, in a simple cubic structure, each particle's coordination number is limited, such as polonium which has a coordination number of six due to its inefficient packing arrangement. In the case of transition metals which can have partially filled d subshells, the complex ions they form may display a variety of colors. These specifics of electron configuration and atomic size play a critical role in determining the stability and characteristics of the crystal structure.