A Cabochon is a polished gemstone with a flat-bottom (or slightly rounded bottom) and a convex or rounded domed top. Cabochons, commonly known as Cabs, are the oldest and most common form of Gem cutting.
The rose cut is a variation of the cabochon where flat facets are polished into the curved surface of the cabochon cut stone.
Checkerboard cut is a technique where the gem stone is cut into a multitude of square facets spaced regularly around the stones surface, giving a 'Checkerboard' effect of light and dark squares when moved in the light.
Unlike the two-dimensional flat facet cuts, the concave cut is three-dimensional. In addition to length and width, this curved cut results in a conical shaped facet, creating depth as well. This third dimension allows the gem to further refract more of the ambient light and return it to the eye as brilliance.