The 182 faces of this polyhedron are 12 regular pentagons, 20 equilateral triangles, 30 regular octagons, 60 rectangles, and 60 kites. I made this using Stella 4d, which you can find at http://www.software3d.com/Stella.php.
A Polyhedron with 182 Faces, Featuring Regular Octagons, Pentagons, and Triangles, as well as Kites and Rectangles
RobertLovesPi.net 