Doubly periodic entangled motifs from planar tilings

Sonia Mahmoudi (Tohoku University)


Doubly periodic weaves and polycatenanes are complex three-dimensional entangled structures made of open or closed intertwined threads embedded in the thickened Euclidean plane. As in knot theory, one prefers to study their properties at the planar scale, where a generating cell of such a doubly periodic diagram is called a motif. In this talk, we will discuss three methods to construct weaving and polycatenane motifs from planar tilings and introduce a way to predict which type of motif can be created from a given tiling and method.

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