Groups, Geometry, and Dynamics

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Volume 7, Issue 2, 2013, pp. 419–442
DOI: 10.4171/GGD/188

Published online: 2013-05-07

Cubulating rhombus groups

David Janzen[1] and Daniel T. Wise[2]

(1) John Abbott College, Sainte-Anne-De-Bellevue, Canada
(2) McGill University, Montreal, Canada

We study CAT(0) 2-complexes all of whose polygons are Euclidean rhombi. We describe walls in these complexes, and examine the dual CAT(0) cube complex. Our viewpoint relates Sageev’s dual cube complexes to de Bruijn’s approach to the Penrose tilings

Keywords: CAT(0) cube complexes, Penrose tilings

Janzen David, Wise Daniel: Cubulating rhombus groups. Groups Geom. Dyn. 7 (2013), 419-442. doi: 10.4171/GGD/188