This isn't my response (yet) but I have an article I found a while ago which (despite the title) is basically a history of the study of polyhedra through 1993. I don't think I can upload the .pdf file, but I can e-mail it if people are interested. It's pretty short and has interesting diagrams.
I mention it because includes the invariant Euler equation we touched upon last week:
V (vertices) + F (faces) = E (edges) + 2.
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