Faceting

Usually this amounts to using a knife or wire to cut off pieces of your workpiece to form several flat, relatively small, surfaces.

You can apply this technique to a leather-hard workpiece that has already been trimmed. You can apply it when handbuilding a piece. Alternatively, you can use it while throwing on the pottery wheel.

When you do that, the flat surfaces you create are distorted while throwing. Not an easy technique, but you can achieve very cool results with it.