The polyhedron above is a faceted pentagonal icositetrahedron. The unfaceted, normal pentagonal icositetrahedron is the dual of the snub cube.

The solid below is a faceted pentagonal hexecontahedron, which, in unfaceted form, is the dual of the snub dodecahedron.

I made both of these models with Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.