Designing a Safe and Crush-proof Pokemon playing card box using a 3D Super-Elipsoid

My friend has two young Pokemon-addicted sons who carry their 60-card playing decks with them everywhere, typically in a cargo pants pocket. Unfortunately, they have either managed to destroy every card box they've tried, or been bruised by sharp corners/edges during other activities.

I thought I could design and print a better one. I started with an inner rectangular box surrounded by a shell having curved edges and corners for safety, and with slightly bulging sides for strength.

Then I researched a bit on getting more crush resistance from the shape itself (rather than adding ever more infill) and found that catenaries are very crush-resistant, as are parabolas.

Then I stumbled into Squircles, the more general Super-Ellipses, and the 3D Super-Ellipsoid. This seems to be exactly what I'm looking for! A closed 3D surface with continuously varying curvature.

[the above edited for clarity by CGW; the next section added in the hopes it will focus answers]

Given that an ideal sphere, and even an idealized ellipsoid of revolution, won't fit nicely in a pants pocket, what general engineering guidelines should [the OP] follow in designing a card box? Rounded corners and edges are a must, to protect fabric and flesh. Are internal ribs on near-flat surfaces a good option?

[end of added material]

The generic form of the 3D Super-Ellipsoid is:

(x/a)^n + (y/b)^n + (z/c)^n = 1

Where: a, b and c are axis scale factors, n is the exponent controlling the shape (2..8, typ. 5-6), and x, y and z are bounded to +/-1

But the above isn't directly usable to create a point cloud.

The parametric form would iterate over three angles. But the problem I'm having is with powers greater than two.

Anyone have some clues to share?

I promise to include a full write-up (including credits from this thread) when I post the final box on Thingiverse. (Perhaps using OpenSCAD?)

BTW, after finding the Squircle I detoured to write a blog post about the characteristics of generalized equations of the form X^n + Y^n = 1

• @CarlWitthoft Would you mind editing this question and focusing the scope here for Engineering? You last saw this question over on 3DPrinting. Thanks!
– user16
Commented May 25, 2018 at 11:37
• @GlenH7 I'll try... Commented May 25, 2018 at 12:25
• Edited to pull in the generic equation from the linked reference.
– BobC
Commented May 25, 2018 at 14:05