What term describes a gemstone cut that has a flat face?

The term that describes a gemstone cut that has a flat face is "cabochon." A cabochon is characterized by its rounded, smooth top surface and usually a flat bottom, which distinguishes it from other cuts that incorporate facets designed to reflect light. These gemstones are typically polished rather than faceted, which can enhance their color and translucence.

In contrast, a dome refers to the arched top surface of a cabochon but does not specify the flat base characteristic. A facet is the flat surface on a faceted gem, typically creating complex light interactions but not applicable to the flat, smooth nature of a cabochon. The crown specifically refers to the upper part of a faceted stone above the girdle, which typically does not have a flat face. Therefore, cabochon is the most appropriate term for a gemstone cut with a flat face.