There are several screwable boxes here on Thingiverse, but I wanted to make one parametric so I could play around with it more easily.

Print the STL file, and use the box.

Or edit the settings in the OpenSCAD file, and make all sorts of boxes.

The interesting settings are:

h = height in mm nw = number of times around that you have to screw the lid to close the box cr = radius of circle that's wiggled around to form the shape w = amount of wiggle. Radius of box = cr+w. t = thickness of wall and base

Edit, generate STL, print.

By default it generates both top and bottom, next to each other (which works great on a Replicator). If you want to maximize size in a square print area, comment out one and leave the other to generate each half and print separately.

Printing tonight, I'll upload a photo tomorrow.