Visible interior: icosidodecahedra
Exterior: dodecahedra and rhombicosidodecahedra
Medium: .gif created using software available at http://www.software3d.com/stella.php
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RobertLovesPi.net 
I love how these things turn.
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Thanks! It’s my favorite recent addition to the software I use for these (“Stella 4d”). =)
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