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:

https://ixxyxr.github.io/polyhydra-web/?m=3

Kusudama is your keyword if you want to learn how to do these :)

The 5 intersecting tetrahedra is particularly cool, and I've used these instructions to assemble it http://origametry.net/fit.html

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.

Also saddened by the lack of Catalan solids

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.

This is not origami.