2.6.1 Generalized tanglesGeneralized ntangles with 2n emerging arcs instead of 4 (n=2) are mentioned in Conway's paper (1970) without a further elaboration. The same holds for Murasugi (1996, page 172): after defining ntangles (called there (n,n)tangles) and giving a sample of a (3,3)tangle, the author continued to work exclusively with 2tangles (or (2,2)tangles). Even the examples of particular ntangles and their use is hard to find. However, we are very familiar with an elementary 3tangle: it is the standard illustration of the third Reidemeister move. A. Caudron (1982) used hyperbolic ntangles for the construction of basic polyhedra, and H. Moriuchi (2004) enumerated thetacurves (i.e., nonalgebraic 2tangles) with up to 7 crossings. Nonalgebraic 2tangles with n £ 11 crossings are considered in preceding section. Generalized tangles will be used in order to extend Conway notation to nonalgebraic tangles and basic polyhedra, describe nonalgebraic tangle types and use a typealgebra for computing the number of components of nonalgebraic KLs.
