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In knot theory, the 6 2 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 6 3 knot. This knot is sometimes referred to as the Miller Institute knot , [ 1 ] because it appears in the logo [ 2 ] of the Miller Institute for Basic Research in Science at the University of California, Berkeley .
An example is 1*2 −3 2. The 1* denotes the only 1-vertex basic polyhedron. The 2 −3 2 is a sequence describing the continued fraction associated to a rational tangle. One inserts this tangle at the vertex of the basic polyhedron 1*. A more complicated example is 8*3.1.2 0.1.1.1.1.1 Here again 8* refers to a basic polyhedron with 8 vertices.
6 8 10 2 4 [5] 12345:12345 Three-twist knot: 5 2: 5a1 4 8 10 2 6 [32] 12345:12543 1231\452354 Stevedore knot: 6 1: 6a3 4 8 12 10 2 6 [42] 123456:216543 1231\45632654
Many knot polynomials are computed using skein relations, which allow one to change the different crossings of a knot to get simpler knots.. In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot.