This skull basket thing is woven with a simple triaxial weaving pattern. I had it printed as a test and although I'm very happy with it, it did show me that a 1 mm diameter wire and such an open weave is a bit too fragile.
The shape is based on a free model by Nosferados called
Calaveras de Azucar (Sugar Skulls).
There are only three components or loops, as you can see in the colored rendering.