  We introduce a construction of affine invariant subvarieties in strata of
translation surfaces whose input is purely combinatorial. We then show that
this construction can be used to construct the Bouw-Moeller Teichmueller curves
and the seven Eskin-McMullen-Mukamel-Wright rank two orbit closures. The
construction is based on the theory of Hurwitz spaces and is inspired by work
of Delecroix, Rueth, and Wright.
