I was wondering if there was a way to recreate this sort of texture on a cylinder. I don't know if it's an actual texture or an actual surface.
Another way to do this :
Select the faces around your cylinder
Add loopcuts (Ctrl+R, mousewheel) to make square faces
In Object mode (Tab) add a decimate modifier on unsubdivide with 1 iteration and apply it
In Edit mode (Tab) select your faces, then inset with i and i again for individual faces
Use Ctrl while inseting to give some thickness or extrude individual faces with Alt+E
You can do it both ways by model or faking the geometry by using a texture.
Starting with a plane extrude two edges so that you get a model like:
Add two Array Modifiers to create a grid:
Apply the modifiers and cut out the part you want to use, then scale it so that the tiles get the diamond shape. I've also selected the faces (by similar area) and beveled them Ctrl-B:
Add again an Array modifier and a Curve modifier:
Now you can decide to use it as geometry or bake it to a texture.