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Construction of weavings in the plane
Author(s) -
Miro Eden Delight,
Zambrano Aliw-iw,
Garciano Agnes
Publication year - 2018
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s205327331701422x
Subject(s) - weaving , disjoint sets , intersection (aeronautics) , net (polyhedron) , plane (geometry) , simple (philosophy) , combinatorics , graph , mathematics , disjoint union (topology) , computer science , discrete mathematics , geometry , engineering , geography , cartography , mechanical engineering , philosophy , epistemology
This work develops, in graph‐theoretic terms, a methodology for systematically constructing weavings of overlapping nets derived from 2‐colorings of the plane. From a 2‐coloring, two disjoint simple, connected graphs called nets are constructed. The union of these nets forms an overlapping net, and a weaving map is defined on the intersection points of the overlapping net to form a weaving. Furthermore, a procedure is given for the construction of mixed overlapping nets and for deriving weavings from them.