Here’s a single dodecahedron.

A new “cluster polyhedron” can be made by augmenting each pentagonal face with another dodecahedron.

If you can do it once, you can do it again, augmenting each pentagon with a new dodecahedron.

Once more.

I made these polyhedral clusters using *Stella 4d: Polyhedron Navigator*, which you can try for free at http://www.software3d.com/Stella.php.

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