Universal Gröbner bases (UGB) are a useful tool to
obtain a set of different models identified by an experimental design.
Usually, the algorithms to obtain a UGB for the ideal of
a design are computationally intensive. Babson et al. (2003)
propose a methodology to construct UGB in polynomial time.
Their methodology constructs a list of term orders based upon
the Hilbert zonotope. We focus on the generation of such a list.
We use results on hyperplane arrangements to present a theorem
which simplifies the computation of term orders for designs in
two dimensions. Our theorem constructs directly the normal fan
of the Hilbert zonotope.
