Forcing lexicographical order in the solutions to an integer programming problem is a possible strategy to avoid symmetric solutions. An orbisack is the convex hull of the lexicographically ordered pairs of n-dimensional binary vectors. In this paper, we present a minimal complete description of orbisacks. In addition, we provide a polynomial formulation with exponential coefficients and a formulation with an exponential number of constraints but with unit coefficients, both of which still force lexicographical order. An exact separation procedure is also described.