This OpenSCAD code generates a Rhodonea curve as described on this Wikipedia page
and extrudes it into 3 dimensions to form a vase or bowl. If you have OpenSCAD, you can download the .scad file to your computer, and use it to design your own vase or bowl.
See the chart on the Wikipedia page for example Rhodonea curves.
petals = n in the chart
amplitude = d in the chart
Besides the default petals=3, amplitude=5, some of the designs I like are
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