Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs
Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's $3^d$ conjecture for such polytopes (they all have at least $3^d$ nonempty faces) and show that the Hanner polytopes among them (which have exactly $3^d$ nonempty faces) correspond to threshold graphs. Our …