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I created this shape in Illustrator and imported the SVG into blender. I want to rotate the flat object by 360 degrees over the Z-Axis to make the object round.I would be pivoting the bend over the flat edge.

I tried creating an empty and adding a twist modifier to and twist over the empty. I also tried adding a simple deform modifier.

My blender object

Blender object

What I want it to look like

3D example final result

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Right of the bat, using an .svg for this purpose is not a good idea, because you're creating a lot of unnecessary topology. You should rather create a circle/cylinder and work your way from there.

But since you asked, I recommend the spin tool in Edit Mode:

Spin

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    $\begingroup$ You can also use the "Screw" modifier set to the "Z" axis and an angle of "360" if you want to go non-destructive. Remember to apply rotation before (CTRL - A). $\endgroup$ – Gorgious Feb 17 at 11:52
  • $\begingroup$ Can you elaborate on this extra topology you are worried about? Can't both approaches end up with identical models? $\endgroup$ – Matt Feb 17 at 13:13
  • $\begingroup$ @Matt I was refering to using an actual .svg file as a base model. The only way I'm aware of creating/using them is, in short, creating a picture and letting Blender draw an edge between every pixel, thus creating an absurd amount of vertices. $\endgroup$ – Zagstrug Feb 17 at 20:20
  • $\begingroup$ @Zagstrug SVG is a vector format, there are no pixels. I just tested importing a similar SVG to the one in the OP and it only ended up in blender with the handful of nodes that I had originally drawn. I think your excess topology fear is unjustified. $\endgroup$ – Matt Feb 17 at 21:06

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