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Although this tutorial is about making vases, it applies equally well to making tumblers. First create a template by wrapping a stiff material around the glass and trimming it to size. Roofing paper works well for making templates for clay handbuilding. Building it over the original glass helps to hold the structure. Baby power can be used instead of a non-stick liquid to help the clay to slide off. Don't forget to add a bottom.
Molds by UnaOdd-Lynn. Used a product called Knead-a-Mold, from Townsend Atelier. It creates a silicone rubber mold that sets in less than 10 minutes. The final mold can be used in the oven (for polymer) and is food safe as well. Polymer clay can be used in the molds. Most molds were made from plants in the garden.