parametric model of platonic solids with playing cards

Hey guys,

I'm trying to create a parametric model of platonic solids made out of rectangles with the same ratio as playing cards. To be more precise i'm trying to recreate the contents of this link:

http://mathcraft.wonderhowto.com/how-to/make-platonic-solids-out-pl...

I'm particularly interested in modeling the icosohedron but I can't seem to figure out how to arrange the rectangles. I thought i'de use weaver bird, deconstruct the polyhedron and use their faces to extract normals from the center and place the rectangles there but im not getting the desired effect. If anyone could help me out i'd really appreciate it. I've attached my file below but don't know if i'm doing it right.