The vase looks like an origami folded object.
It looks like 3 cones, or frustums of cones.
Maybe it is developable.

I did a simple pleat .3dm. Basically just triangles, non-equilateral tetrahedrons.
Fillet will work on it at .2 units.

After some fillet, maybe it could be bent or flowed, then circular arrayed?


- Brian