  Diagrammatic sets are presheaves on a rich category of shapes, whose
definition is motivated by combinatorial topology and higher-dimensional
diagram rewriting. These shapes include representatives of oriented simplices,
cubes, and positive opetopes, and are stable under operations including Gray
products, joins, suspensions, and duals. We exhibit a cofibrantly generated
model structure on diagrammatic sets, as well as two separate Quillen
equivalences with the classical model structure on simplicial sets. We
construct explicit sets of generating cofibrations and acyclic cofibrations,
and prove that the model structure is monoidal with the Gray product of
diagrammatic sets.
