Polyhedral image created with Stella 4d, available at http://www.software3d.com/stella.php.

Software credit:  http://www.software3d.com/stella.php

Visible interior: icosidodecahedra

Exterior: dodecahedra and rhombicosidodecahedra

Medium: .gif created using software available at http://www.software3d.com/stella.php