The more faces added to a roof the more complicated the framing becomes and 99% of the time you will have to pay a significant increased cost for it. As you increase the number of faces and angles on a roof line the major increase is the time it takes to frame complicated angles and shapes.
It’s important to keep in mind that you’ll need to plan out a roof design that will provide a good sized overhang for drainage, runoff, and wall protection. This is very essential if you want to stretch the protecting overhang above the walls.
There are other cost effective roof styles like a two sided triangular roof, a roof which is more bell shaped when viewed from the side, a roof which is in the shape of a pyramid, or a roof that’s two-sided and similar to the first one but with only two sides.