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A description is given of 4-connected nets with one kind of vertex in which the shortest rings containing each pair of edges are N-rings (N > 4). Eleven uniform nets (66) are identified; seven of these are believed to be new. A further thirteen nets with one type of vertex and without 3- or 4-rings are described; nine of these are also believed to be new
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O’Keeffe et al. (1992) studied this question.
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