This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture chemistry, biology (or even jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from basic polyhedra: mid-edge construction, cross-curve and double-line covering, and edge doubling construction. These methods are implemented in the Mathematica-based program LinKnot and can be applied to the data base of basic polyhedra. In a similar way, an edge doubling construction transforms fullerene graphs into alternating knot and link diagrams. In the last part of the paper is proposed the use of virtual knots and links and the corresponding nonplanar graphs obtained from their Gauss codes.
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