I made this twist vase with OpenSCAD with the intention of making something that would reflect light from many angles while being rotated. It's an octagon that's been linearly extruded upwards with a bit of rotation every few millimeters. Each "layer" of the vase is scaled (width-wise) based on a sine wave.

In other words, this vase is math.

Print instructions

Print it in vase mode or just tell your slicer to use 0% infill and 0 top layers. The amount of perimeters/walls and bottom layers is up to you! It should be water tight even in vase mode... If it isn't then you might want to increase the extrusion width or the number of perimeters (or just apply a drop of glue to where it leaks which is probably just going to be the transition from the top bottom layer to where it starts spiraling upwards).

Recommended layer height: 0.12-0.16mm seems to be the magic number for most filaments.  You can go finer (e.g. 0.1mm) but with many filaments that results in a loss of sheen/shine.  PETG and “silk” filaments seem to be impacted the most by this.  For reference, I pretty much always use 0.16mm 👍