Medial Rhombic Triacontahedron
Dual of the dodecadodecahedron, and a
stellation of the rhombic triacontahedron.
This model could really have done with some sort of internal support, and is
quite flexible without it.
Here's a topological version. In this version parts of each
face have been cut away so that only faces that truly share an edge are
still connected. Where two faces would normally intersect to cause a
false edge, now they weave through each other without collision.