A faceted girdle is one where the brillianteer polished facets into the diamond's girdle. Very normal.
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An unfaceted, or bruted girdle is one where the diamond's girdle is unpolished and has a frosted appearance. Some cutters believe polishing the girdle may cause color to be reflected back inside, so unfaceted girdles are common in J or K color grades and down, and in small goods, .25 and lower. In near-colorless diamonds it's not the concern that it is with slightly colored and below.
A polished girdle on a diamond is see-through or clear. A polished girdle is considered a finishing touch but is not critical. One situation where polish is desirable is when the diamond is a fish-eye, where polishing will reduce the effect of the girdle's reflection in the table.
New machines have been developed that are putting a fine finish on girdles. These diamond girdles are more than bruted, but less than polished. We choose to call these finely finished: It is not faceted, not completely polished, nor does it remain bruted. It is in a warm and cozy place somewhere in-between.