Designed to test out a transparent resin on my msla printer! I have successfully printed 3 so far - one at this size and a couple scaled a bit larger. I had some hiccups in the modelling stages so the method is a tiny bit hacked together - here's what I did, if you want to make your own variation (I used Rhino 6):

• Draw a "rail curve" on the xy plane, I chose a 20-pointed star. It needs to stay flat in the Z direction, and it needs to be "closed" - the start and end should link up.
• Draw a "profile curve" on the xz plane. This decides the side-on view of your vase, and it should connect to the right- or left-most side of your rail curve.
• Use the "Revolve" command, with an angle of 360
• Cap Planar Holes. At this stage, I had a solid pumpkin looking object.
• Copy the object and put the second one a known distance away, so you can easily put it back exactly where it was. I use grid snap for this so I know it's a multiple of 1mm away
• Run the "Twist" command on one, set the rotation axis as going from the centre of the bottom of the object to the centre of the top. It might help to enable "ortho" in the snapping options at the bottom of the screen. Then disable ortho and from the top view, click somewhere to the side of the object and move clockwise around the axis until you like the level of twistyness, then click again to confirm.
• Repeat this process with the second object, but go anticlockwise this time
• Move the second object back to where it started
• "Boolean Union" both solid objects together
• This is where things started getting weird. The shell command didn't like it, and neither did offset surface. Those are the standard ways to do this.
• For this specific vase I had to extract surface on the top surface, making a vase with no "thickness"
• Then, copy in place, select one of the copies and scale it down. My vase is 35mm high and the width is similar so to get a wall thickness of a little over 1mm I scaled it by a factor of 0.93, placing the reference point on the xy plane in the middle of the base. I then measured the distance from the top of the larger polysurface to the top of the smaller one, halved it, and then moved the smaller one upwards by this amount. This isn't the right way to do this but when offsetSrf is creating strange spheres on all the corners of your vase it works in a pinch!

In my tests it hasn't needed any supports using a resin printer - I don't know if it would work in fdm - I'd love to see your results if you try it!