How to model component pieces of a geometric solid? I'm trying to make a model of the first atomic bomb's high explosive lens configuration:



The shape is a truncated icosahedron composed of extruded octagons and pentagons. 

Modeling a single solid truncated icosahedron is easy — there are lots of tutorials out there under "how to model a soccer ball" (make an icosphere, apply a single subsurf to it, tweak the center of the vertices a little). 

But I'm struggling to see how I can turn something like that into a model that is composed of the 32 separate 3D octagons and pentagons.

So far I've tried making a truncated icosahedron, extruding it, deleting the all of the shapes except one pair of inner/outer octagons, connecting their edges manually (since extrude won't for such a complex shape)... which is a very slow and tricky process (it's a lot of vertices/edges to wade through for each shape).

Is there a better way that I am missing? If I had one octagon and one pentagon, would it be then easy to have them tile around the sphere in this way? (I haven't been able to manage it with Array or Mirror; the angles seem just a little too eccentric for the transformation defaults).

Any suggestions would be appreciated.
I accomplished this. I have removed some of the facets to show the inner side.



This is how:


Make a football (as you said, subsurf an icosahedron, dissolve all vertices on middle and edges).
Add the edge split modifier with split angle 1. This will make each ngon (pentagon and hexagon) separate from its neigbours.
Apply the modifier.
Go into edit mode and select all faces.
Extrude all faces but right click directly. This will make them double but select all faces that will form the outer shell.
Scale out the selected faces.