Construction of weavings in the plane

• Main Authors: Miro, Eden Delight, Zambrano, Aliw-iw, Garciano, Agnes
• 格式: text
• 出版: Archīum Ateneo 2017
• 主題: tilings; triangle groups; colorings; nets; weavings; Geometry and Topology; Mathematics
• 在線閱讀: https://archium.ateneo.edu/mathematics-faculty-pubs/15; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1014&context=mathematics-faculty-pubs

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.