These girih polyhedra have 32 faces. They're related to the quasiregular polyhedron, the icosidodecahedron. They include 2 decagon and 10 elongated hexagon faces, as well as triangles. The decagon and elongated hexagon are decorated with the girih tile pattern. A similar pattern continues across the triangles.
32 Faces with Girih Pattern
32 Faces with Wireframe Girih Pattern