  This paper starts a systematic description of colored knot polynomials,
beginning from the first non-(anti)symmetric representation R=[2,1]. The
project involves several steps: (i) parametrization of big families of knots a
la arXiv:1506.00339, (ii) evaluating Racah/mixing matrices for various numbers
of strands in various representations a la arXiv:1112.2654, (iii) tabulating
and collecting the results at www.knotebook.org. In this paper we discuss only
representation R=[2,1] and construct all necessary ingredients that allow one
to evaluate knot/links represented by three strand closed parallel braids with
inserted double-fat fingers. In particular, it is used to evaluate knots from a
7-parametric family: this family contains over 80% of knots with up to 10
intersections, but does not include mutants.
