Surface decorations in clay pieces include incising, carving, fluting, and faceting. Used by themselves or in conjunction with other decorative techniques such as glazing, these offer a wealth of possibility in creative clay work.
Support the area below the area to be removed, either with your hand directly if using a dull blade, such as a fettling knife, or with a piece of wood if using a sharper blade. This support will help keep the end of the cut clean, with no ragged tear-aways.
When creating fairly large facets, grip the knife blade at both ends to help keep the knife steady and moving smoothly. For even facets around the pot, cut the first one, then turn the pot 180 degrees, cut the next facet at the same angle, turn the pot 90 degrees, cut the next facet, turn the pot 180 degrees to cut the fourth facet, and so on.