It should probably be noted somewhere that this is more "papercraft" than "origami", and the thing you download is just the net of the solid, not instructions to make what's in the picture.
Some of the platonics have folding instructions not just the papercraft net but yeah I wish some of the more interesting ones had actual instructions for the thing being shown too.
I looked at the page, and decided I wanted to see how to origami some of the archimedian solids, which are lower down the page. I don't find platonic solids as interesting so I didn't click on them. I saw they existed but you can't see that they have folding instructions unless you click on them
At the danger of spamming this (well - posting it for the second time in 6 months) - I'm still trying to find the select demographic who appreciate this:
I was lucky enough to meet the guy behind mathigon for dinner a long time ago. He's brilliant! I'm always excited to see what he is up to! Glad to see this voted up.
Also saddened by the lack of Catalan solids
The 5 intersecting tetrahedra is particularly cool, and I've used these instructions to assemble it http://origametry.net/fit.html
https://ixxyxr.github.io/polyhydra-web/?m=3