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math.GT2022★ 1 cited
Construction of weaving and polycatenane motifs from periodic tilings of the plane
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions…
math.GT2022
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
A weave is the lift to the Euclidean thickened plane of a set of infinitely many planar crossed geodesics, that can be characterized by a number of sets of threads describing the o…