The clever thing is that in the base of the vase, where the NeoPixel ring nestles, are the ends of 16 lengths of 2.85 mm transparent PETG filament. These guide the lights (which are, of course, programmable) in a spiral shape around the surface of the vase.
You can find out more about this build by maketvee at https://www.instructables.com/The-Neopixel-LED-Vase/