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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. © 2007 Elsevier Inc. All rights reserved.
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