  We construct algebras from rhombohedral tilings of Euclidean space obtained
as projections of certain cubical complexes. We show that these `Cubist
algebras' satisfy strong homological properties, such as Koszulity and
quasi-heredity, reflecting the combinatorics of the tilings. We construct
derived equivalences between Cubist algebras associated to local mutations in
tilings. We recover as a special case the Rhombal algebras of Michael Peach and
make a precise connection to weight 2 blocks of symmetric groups.
