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Can you recommend any books or survey articles on $01$-polytopes, thats is, polytopes with vertices in $\{0,1\}^n$?

I am less interested in random $01$-polytopes, but more in the combinatorial structure of these, which polytopes can be realized as $01$-polytopes, their symmetries, their combinatorial types, interesting families of examples one should know, ...

There seems to be a flood of articles out there, but I am not aware of any book to start reading about a general theory. I suspect that sources on lattice polytopes might work as well, but the questions one might ask for this more general class are often different. But maybe some book/article on these contains a section devoted to $01$-polytopes.

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There's Ziegler's 1999 Lectures on 0/1-Polytopes, a 45 page survey on the arXiv. It is also the lead chapter in Polytopes - Combinatorics and Computation, Birkhäuser, 2000.

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