Title: On the Complexity of Polytopes in $LI(2)$,
Abstract: In this paper we consider polytopes given by systems of $n$ inequalities in
$d$ variables, where every inequality has at most two variables with nonzero
coefficient. We denote this family by $LI(2)$. We show that despite of the easy
algebraic structure, polytopes in $LI(2)$ can have high complexity. We
construct a polytope in $LI(2)$, whose number of vertices is almost the number
of vertices of the dual cyclic polytope, the difference is a multiplicative
factor of depending on $d$ and in particular independent of $n$. Moreover we
show that the dual cyclic polytope can not be realized in $LI(2)$.