I have been exploring folded regular polyhedra, but came across this, a brilliant cut faceted diamond by Satoshi Kamiya and thought I would give it a go:

As a first fold, this is pretty sloppy to be honest – only after finishing it did the geometry I was laying down in pre-creases make sense. I have no doubt that when i re-fold this it will be much nicer.

This fold is a very clever bit of geometry, based on an octagonal piece of paper, making many facets and that classic jewellery diamond shape (this one would be a few hundret carats at that). The top face facets are locked in place by tiny closed sinks (making this very difficult I suspect to fold really small).

It is a pity there is no real locking mechanism to keep the model closed (I cheated and used a little sticky tape) – the bulk of paper does swirl in place but tends to spread when left – this might be different if made with a foil paper.

I seem to be folding a bunch of Kamiya models at the moment – prolly inspired by my latest Origami book purchase