Miller Institute Knot


The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is implemented in the Wolfram Language as KnotData[{6, 2}].

Miller Institute logo

The knot is so-named because it appears on the logo of the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science at the University of California, Berkeley (although, as can be seen in the logo, the Miller Institute's knot actually has dextro chirality).

The knot has braid word sigma_1^(-1)sigma_2sigma_1^(-1)sigma_2^3. It has Arf invariant 1 and is not amphichiral, although it is invertible.

The Alexander polynomial Delta(x), BLM/Ho polynomial Q(x), Conway polynomial del (x), HOMFLY polynomial P(l,m), and Jones polynomial V(t) of the Miller Institute knot are

del (x)=-x^4-x^2+1

No knots on 10 or fewer crossings share the same Alexander polynomial, BLM/Ho polynomial, or Jones polynomial with the Miller Institute knot.

See also

Figure Eight Knot, Knot, Prime Knot, Solomon's Seal Knot, Stevedore's Knot, Trefoil Knot

Explore with Wolfram|Alpha


The Adolph C. and Mary Sprague Miller Institute for Basic Research in Science. University of California, Berkeley., D. "The Knot 6_2." "6_2."

Cite this as:

Weisstein, Eric W. "Miller Institute Knot." From MathWorld--A Wolfram Web Resource.

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