As is often the case with tessellation it looks magical and I think ‘aperiodic’! ‘Penrose’! Yeah! But it turns out that this is a rather simple tessellation after all. Sorry to have misled you. Will post the steps to repro this in just a few.
So very quickly: add a dodecahedron. You can add the standard one, then join each pair of faces to make them into pentagons then poke faces then to sphere. Or you could just save yourself a lot of work and add a ‘pentakis dodecahedron’ with all this work done for you already.
Optionally you could go from step three (poke faces) straight to step seven, skipping the spherization. This will give you a flatter ‘star’. Your example probably has flat ‘stars’.
Now each triangle has to be subdivided with two cuts, dividing each side into three. hen dissolve some edges and use J to join the unconnected vert to the center. Now - ha! - do this for every triangle on your solid. There are 60.
You can also try duplifacing to see if you can make the geometry separately and distribute it all in one action. Good luck.
Once you have the new geometry in place you can bevel and delete the faces etc. as described above and in many places.