Intersection() and regular solids

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Intersection() and regular solids

I'm just starting to learn OpenSCAD and having great fun with it - many thanks to all the developers.

I'm interested in the problem of how designers learn to choose an approach to the construction of an object from the primitives and available operators, in particular using the less natural operators like intersection, minkowski and hull.

The wikibook shows an example of using intersection to construct a dodecahedron   but I don't know where this construction comes from.  Playing around, I found I could construct an octahedron using the same approach :  and I feel it should be possible to construct others this way. 

I'd welcome any pointers on the theoretical base for this construction and ideas for other solids.  I like the approach because its more concise than the polyhedral approach I've seen.

Chris Wallace