These two girih polyhedra are a 32-faced icosidodecahedron and the related pentagonal orthobirotunda. They each include 12 pentagon and 20 triangle faces. The pentagons are decorated with the girih tile pattern. A similar pattern continues across the equilateral triangles.
Icosidodecahedron Wireframe Girih Pattern
Icosidodecahedron with Girih Pattern
Pentagonal Orthobirotunda Wireframe Girih Pattern
Pentagonal Orthobirotunda with Girih Pattern