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Figure 1
Eleven topologically distinct types of planar tilings in their most symmetric representation. Each type is characterized by the vertex valences and by the space-group symmetry (in parentheses). 4444 (p4mm), 333333 (p6mm), 666 (p6mm), 884 (p4mm), 44333 (c2mm), 43433 (p4gm), 6363 (p6mm), 6434 (p6mm), 1264 (p6mm), 12123 (p6mm), 63333 (p6).

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