Below is my process of designing this vase in Fusion 360. The commands I used included sketch, revolve, offset surface, split, extrude to make the hole, extrude for intersecting, shell, sketch project to the body, parallel constraint, and circular pattern.
In the beginning, I sketched the vase and used revolve to create the body. Then, I offset the top and bottom surfaces and used them for the split. Now, I have three bodies. The top body needs a hole, so I created another sketch on the top surface and extruded it along the body. For the middle body, I applied the shell command. Then, I made a project sketch on this body, creating two parallel lines. By extruding this surface on both sides, I created the intersection. Finally, I used a circular pattern to make this interesting shape.
The last step was adding some bevels and combining the bodies.
I imported this model into Blender and added lighting and textures.
Here are my rendered vase images:
