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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 .
Figure-eight knot: 4 1: 4a1 4 6 8 2 [22] 1234:2143 1231\4324 Cinquefoil knot: 5 1: 5a2 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 6 2 knot: 6 2: 6a2 4 8 10 12 2 6 [312] 123456:234165 1231\45632456 6 3 knot: 6 3: 6a1 4 8 10 ...
The Dowker–Thistlethwaite notation for this labelling is the sequence: 6, −12, 2, 8, −4, −10. A knot diagram has more than one possible Dowker notation, and there is a well-understood ambiguity when reconstructing a knot from a Dowker–Thistlethwaite notation.
2,3 torus (or trefoil) knot has a stick number of six.. In the mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot.
Like the figure-eight knot, the 6 3 knot is fully amphichiral.This means that the 6 3 knot is amphichiral, [2] meaning that it is indistinguishable from its own mirror image. In addition, it is also invertible, meaning that orienting the curve in either direction yields the same oriented knot.
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.
Knitting abbreviations can be grouped by what they describe: side of work; RS and WS signify the "right side" and "wrong side" of the work.. type of stitch; k means a knit stitch (passing through the previous loop from below) and p means a purl stitch (passing through the previous loop from above).
Mosaic knitting is a form of slip-stitch knitting that knits alternate colored rows and uses slip stitches to form patterns; mosaic-knit fabrics tend to be stiffer than patterned fabrics produced by other methods such as Fair-Isle knitting.
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