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A video demonstration of prefolded patterns:



Like I mentioned before, the Fujimoto method is one of the most elegant solution without glueing and cutting. Now I'll demonstrate how to fold a hexagonal 6-sided cup. It's easier to fold than the 12-sided hyperboloid cup.
You can use it for your pencils. Besides this construction is rock solid, it can hold a dictionary.

The same method is used for the other geometry shapes. If you study the pattern of the antiprism, the bottom of the prism is shifted by 1/2 length and the sides of the object are converted into equilateral triangles so that it does result as an antiprism. The folding structure of the closure is equivalent to the lower half part of the bottom.

The cube-octagon hybrid is combined with octagon + square frame (base). 

Step 1: Crease Pattern

Here are the CPs for the cup and box.

-mountainfolds (blue)
-valleyfolds (red)
 
Wow! That is sturdy! I would have thought it would crumple under that book. You should enter this into the Holiday Gifts Contest!
sphere360 (author)  Penolopy Bulnick2 years ago
Thx for the tip!