If there is anybody interested in modelling geometric sculptures, I wrote I brief tutorial that illustrates one of the possible methods to obtain this kind of models.
First. Choose a somewhat symmetrical polihedron as a basis for your model.
For instance: Platonic, Archimedean and Catalan Solids they all work fine.
They're quite easy to draw but you may of course download them from the 3DWH.
(Interestingly engough all those solids can be modelled without ever having to type in any measures for sides or angles! Sketchup is so powerful).
In this brief tutorial I'm going to choose the Truncated Icosahedron, that is:
the soccer ball:

Second. Choose two or more edges of your polyhedron. It is easier for the subsequent steps if the edges you choose are coplanar (that is, there is a plane that contains them all) but you can also choose non-coplanar edges.
In this example I'm going to choose the edges shown in the image:

Three. Create something that connects the edges you've choosen.
If you want a nice result, it is better to draw something symmetrical. In this example, we have to connect three edges, so I've drawn a component with three-fold simmetry.

Four. Copy the component that connects the edges in all possible positions,
until you've covered every edge of the polyhedron.
You may now want to modify the connecting component to avoid collisions.
Then erase the polyhedron and just keep the connecting components (skp file attached):

cagework_2.skp