Flattening Section of Cylinder (?)

Hey There,

There's a certain effect I'm trying to get with this cylindrical part I'm creating, but I really don't have any idea how I can achieve it. This image is the effect I'm trying to get ( but with a cylinder)
http://decoration-ideas.org/interior/wp-content/uploads/2011/06/Design-modern-Vases-and-outdoor-lighting.jpg

So far I've managed to create the cylinder and wrap a diamond shape around the cylinder (then linear + circular pattern it around the cylinder) but the individual diamonds aren't as flat as they are in the picture above. I want to create a very geometrical, polygon type look. Does anybody have any idea how I would possibly "flatten" out the individual diamonds on the cylinder so they're not as curved?

(This is what I have so far)

I've attached the solidworks part as well.

Any help would be much appreciated, thank you for looking at this!

Dara

SolidworksParts And Features