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Figure 1
A flowchart depicting the enumeration process and the relationships between different classes of tilings and nets considered here. 1: Unfold the D symbol within a specific subgroup chart (many-to-many) (§4[link]). 2: Find the minimal-image (maximal-symmetry) D symbols (many-to-one) (§6.1[link]). 3: Map the hyperbolic tiling onto a tritorus (one-to-one) (§5.3[link]). 4: Embed the tritorus, remove faces, leaving edges in three-dimensional space (§6.4[link]). 5: Map the hyperbolic tiling onto a triply periodic minimal surface (one-to-one) (§5.1[link]). 6: Remove faces, leaving embedded edges and vertices (many-to-one) (§6.2[link]). 7: Find the canonical, maximally symmetric form for the e-net topology (many-to-one) (§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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