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Figure 9
Illustrations of duality. Each column shows a tile-2-transitive tiling above its dual vertex-2-transitive tiling, together with orbifold and tiling class labels (where F, S and G refer to the fundamental tiling, split and glue operations, respectively). The tilings with symmetry [\star{\tt 266}] illustrate the general case in which the dual D symbol is not present in the initial tile-transitive enumeration. In contrast, the tilings with symmetry [\star{\tt 344}] are both tile-2- and vertex-2-transitive. Each is generated via a different FSGG sequence applied to the [\star{\tt 344}] fundamental tiling, and this pair of tilings is called `mutually dual'. The third column of tilings with symmetry [\star{\tt 2323}] shows a self-dual example.

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ISSN: 2053-2733
Volume 65| Part 2| January 2009| Pages 81-108
doi:10.1107/S0108767308040592
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