I goofed around with OpenSCAD tonight and came up with a little module that I'm using to create models to be printed in vase mode on my 3D printer.

You can find the STL files on Thingiverse - cerkit Vase #1.

My first vase as it was printing:

Vase 1 on the print bed

Here's the module code to create a vase. Unfortunately, it requires a bit of post-processing to get it upright and trim off the unused bottom and top.

// vase.scad
// Draws the vase
module vase(pointCount, h, radiusMultiplier, cubeXY)
{
	for (i = [1:pointCount]) {
		angle = i * 360 / pointCount;
		edgeRadius = pointCount * radiusMultiplier;
		rotate(angle, [1, 1, 1]) {
			minkowski() {
				cube([cubeXY, cubeXY, h]);
				// rounded corners
				cylinder(h = h, r = edgeRadius);
			}
		}					
	}
}

Here are the parameters for vase 1 above:

// vase 1

include <vase.scad>;

// vase(pointCount, h, radiusMultiplier, cubeXY)

vase(32, 75, 3, 300);

Here's a picture of the finished vase:

Vase 1

I threw this together in about an hour, so it's not as solid as I'd like. Maybe I can get it where it's a modifiable Thing on Thingiverse. Who knows, it was just a fun evening project for now.