The Combinatorics of Interval Vector Polytopes

An interval vector is a (0, 1)-vector in Rn for which all the 1’s appear consecutively, and an interval-vector polytope is the convex hull of a set of interval vectors in Rn. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle.