Seminar Geometrija, vizuelizacija i obrazovanje sa primenama, 10. mart 2011.

Naredni sastanak Seminara održaće se u četvrtak, 10.3.2011, u sali 301f Matematičkog instituta, Knez Mihajlova 36.

Predavač: Slavik Jablan

Naslov: Polyhedral Knots and Links

Apstrakt: Indonesian weaving and Tamari balls inspired the original tensegrity researchers, B.Fuller and K. Snelson. In a few last decades, the use of light-weight materials, tensegrity and computer design (CAD/CAM) tools enables the application of different knots and links (KLs) in architecture. From the point of view of organic chemistry, molecular biology, or architecture the most interesting are complex knotted and linked structures with a high degree of symmetry. However, tabulation of KLs as well as computing of KL invariants is restricted to KLs with relatively small number of crossings. We give a survey of different methods for obtaining knots and links in the form of different geometrical polyhedra, that can have applications in chemistry or architecture. Together with the LinKnot data base of basic polyhedra we use several constructions: mid-edge construction, cross-curve and double-line covering, Jaeger construction, and edge doubling construction to obtain 4-valent polyhedral graphs and their corresponding knots and links. In the same manner, edge doubling construction is applied to fullerene graphs to transform them into alternating knot and link diagrams.

 


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