So I was messing with a low-grade triangle grid and what to do with it (I often fold grids to keep my eye in) and came across a rather neat geodesic hemisphere that used a section of it:

So I cut 2 the same size and proceeded to collapse – one fits inside the other and makes a rather lovely icosahedral prism box.

Designed by Hideo Kumayama, I love the lines of this shape, a lovely little tennis ball sized prism that opens – I wonder what you could put in it?

The pre-creasing is everything on this model – with the right orientation of creases, the shape evolves quite naturally, and is locked in place by a unit overlap and an internal twist which is lovely.