The 59 stellations of the icosahedron are very nice polyhedra.
We still met half a dozen of them: (see the Du Val's notation) Among the others, here are my favorite, with LiveGraphics3D.

A B C Ef11 Ef1 G 
the icosahedron itself
the first stellation the compound of five octahedra the compound of five tetrahedra the compound of ten tetrahedra the great icosahedron (Poinsot star) 
De2f2 

Ef2 

e1  e2f2  
f1  De2f1  
f2  the only disconnected stellation 
H  the complete icosahedron (final stellation) 
references: 
• Polyhedra par Peter R. Cromwell (pages 267280), Cambridge University Press, 1997.
• http://www.georgehart.com/virtualpolyhedra/stellationsicosahedroninfo.html by George W. Hart. (the data used for these images are extracted from VRML files by George W. Hart) 
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