  We describe the explicit form and the hidden structure of the answer for the
HOMFLY polynomial for the figure eight and some other 3-strand knots in
representation [21]. This is the first result for non-torus knots beyond
(anti)symmetric representations, and its evaluation is far more complicated. We
provide a whole variety of different arguments, allowing one to guess the
answer for the figure eight knot, which can be also partly used in more
complicated situations. Finally we report the result of exact calculation for
figure eight and some other 3-strand knots based on the previously developed
sophisticated technique of multi-strand calculations. We also discuss a formula
for the superpolynomial in representation [21] for the figure eight knot, which
heavily relies on the conjectural form of superpolynomial expansion nearby the
special polynomial point. Generalizations and details will be presented
elsewhere.
