Below is a slide show of the construction of a rhombicosidodecahedron.  It is made out of 12 regular pentagons, 20 equilateral triangles and 30 squares.  I was inspired to make the model by the wonderful book Polyhedron Models by Marcus Wenninger, and by the fact that the zometool uses a slightly irregular one of these as the ball that connects the rods together! It was a pleasure to make!!

Here is another way of making a rhombicosadodecahedron using playing cards, and you can make one using slide-togethers!