Second version in a better colour. Outside shell is a single wall.
model is here https://www.youmagine.com/designs/twisted-templar--2
not sure how useful it is as a vase, but it sure looks cool
That was the point. To make something that looks cool. I make make a deeper one to use on my desk to corral my pens.
I also wanted to see if I could redesign the first version to print cleaner. The first version blobbed out the sharp corners. On the new model, I put small radii at the tips, and the slicer handled this geometry much better, and cut the print time by 60%.
I did that, but it did not spiral up the wall. It laid single layers and randomised the start positions.
My greatest concern with this iteration, was to see how changing the sharp corners to small fillet Radii(0.3mm) would affect the print quality. It made a large difference at those sharp tips, as they are not so blobby looking. A good exercise in design for printability. Even if I were to increase those fillets a hair(another 0.2 to make them 0.5mm) there would be even greater improvement.
I also need to work on my technique for removing models as this one left the base behind on the build platform 
I may print one tonight maybe 25mm higher at a slower print speed to allow for better interlayer bonding.
There was no retraction on those corners. There was a double line of filament deposited there. I think the outside was remelted and blobbed over in the process.
Also with the sharp corner in the geometry, there may be a brief pause where the machine changed direction almost 180 degrees while the filament was still being extruded.
With the radius in the toolpath, there is no pause as the change of direction is smoother. I will reprint with a larger radius tonight and compare all three results.