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Figure 14
The orbifold [\star{\tt 2^5}] appears as two distinct subgroups of [\star{\tt 246}]. The top row shows the tilings resulting from the subgroup labelled [\star{\tt 2^5}({\rm a})] in Table 3[link]; the bottom row shows analogous cases for [\star{\tt 2^5}({\rm b})]. Fundamental tilings in the hyperbolic plane for each subgroup are illustrated on the left. In each case we show a single tile broken into [\star{\tt 246}] triangles and a highlighted translational domain. The central column displays fundamental tilings wrapped onto the P surface using the covering map, forming E-tilings (whose edges and vertices describe e-nets). The irregularly shaped unit cells correspond exactly to the highlighted region in the hyperbolic plane images to the left. The right column shows s-nets derived from the E-tilings by forming the most symmetric Euclidean embeddings of the e-net topologies. Tiling and net labels are described in §§5.1[link] and 6.3[link].

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