There's one by Luisa Canovi, made of five modules from A5 paper
http://www.giladorigami.com/origami-database/Icosahedron%20Luisa%20Canovi

a long time ago I used it to make a giant d20:
https://enricap.deviantart.com/art/oversized-d20-5092494
https://enricap.deviantart.com/art/origami-dice-set-6966057
but it's not very stable, it works well for smaller polyhedra but the
icosahedron falls apart easily. However it's pretty easy to tape in
from the inside, if you are willing to cheat ;)

By looking for it, I found this page where you can download the
handouts from a course Luisa held
http://officine.fabriano.com/origami-le-dispense-di-luisa-canovi/ (in Italian)
It includes a module by Pietro Macchi which can be used to make an
icosahedron, each face is made by two halves. I haven't tried it
myself and I'm afraid it's going to have the same problem: good with
fewer units but not so much with a lot of them

all the best,
enui

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