Deformation cones of 2-cubical combinatorial zonotopes

Abstract: We prove that the dimension of the deformation cone of any polytope combinatorially equivalent to a 2-cubical zonotope is bounded above by the number of generators of the zonotope. This bound is tight, and we show that it cannot be improved to an identity. We further extend our results to any 2-cubical polytope whose normal fan is combinatorially isomorphic to a pseudohyperplane arrangement, but we show that it cannot be extended to arbitrary 2-cubical polytopes.