Today I'll show you how to make a hyperboloid cup for my first instructable (Paper Egg)
The great thing is you don't need to glue and cut (except of two for the right format). But maybe it's a bit hard for you to make it, unless you don't have folding experiences.
This model is based on the fujimoto cube method. Kasahara discovered the mathematical solution, how to use the method for several kinds of prisms and polygons. I would recommend to read the book "Amazing Origami" by Kasahara
Step 1: Crease Pattern Description
-blue: mountain folds
-black: cutting edges
Step 2: Folding Instructions
Step 3: The Bottom
Step 4: Cup Modelling
From the top you see the notations A, B, C (D is not important)
Bring A to the outside and B to the inside like shown in the pic.