Faceted Cylinder

Hello all! 

I'm doing my masters in architecture right now, and I've recently been experimenting with grasshopper. I have a problem that I'm working on, wondering if anyone here can lend some ideas. I need to make a faceted cylinder, sort of like the image attached (an old starbucks holiday mug).

In my own experiments, I've gotten as far as making a flat or slightly curved surface have facets, using a random height generator and delaunay triangulation, but as soon as the surface curves back around on itself (like the surface of a cylinder) the function doesn't work. 

If anyone can think of a way to make the facets move outwards around a cylinder, that would be much appreciated!

Thank you in advance!