We propose a computational, convex hull free framework that takes advantage
of the combinatorial structure of a zonotope, as for example its symmetry
group, to orbitwise generate all canonical representatives of its vertices. We
illustrate the proposed framework by generating all the 1 955 230 985 997 140
vertices of the $9$-dimensional White Whale. We also compute the number of
edges of this zonotope up to dimension $9$ and exhibit a family of vertices
whose degree is exponential in the dimension. The White Whale is the Minkowski
sum of all the $2^d-1$ non-zero $0/1$-valued $d$-dimensional vectors. The
central hyperplane arrangement dual to the White Whale, made up of the
hyperplanes normal to these vectors, is called the resonance arrangement and
has been studied in various contexts including algebraic geometry, mathematical
physics, economics, psychometrics, and representation theory.