Associators with Frozen Feet

The Goal

The purpose of the paperlet is to find an explicit formula for an associator with frozen feet. As I'm starting to write, I don't know such a formula. My hope is that as I type up all the relevant equations, a solution will emerge. I'll be just as happy if it emerges in somebody else's mind, provided (s)he shares her/his thoughts.

An associator is a solution $\Phi \in A_{3}$ of the pentagon equation and the hexagon equations ([Drinfeld_90], [Drinfeld_91], [Bar-Natan_97]):

[Pentagon]

$\Phi ^{123}\cdot (1\otimes \Delta \otimes 1)(\Phi )\cdot \Phi ^{234}=(\Delta \otimes 1\otimes 1)(\Phi )\cdot (1\otimes 1\otimes \Delta )(\Phi )\quad {\mbox{in}}\quad A_{4}$,

[Hexagons]

$(\Delta \otimes 1)(R^{\pm })=\Phi ^{123}\cdot (R^{\pm })^{23}\cdot (\Phi ^{-1})^{132}\cdot (R^{\pm })^{13}\cdot \Phi ^{312}\quad {\mbox{in}}\quad A_{3}$.

References

[Bar-Natan_97] ^  D. Bar-Natan, Non-associative tangles, in Geometric topology (proceedings of the Georgia international topology conference), (W. H. Kazez, ed.), 139-183, Amer. Math. Soc. and International Press, Providence, 1997.

[Drinfeld_90] ^  V. G. Drinfel'd, Quasi-Hopf algebras, Leningrad Math. J. 1 (1990) 1419-1457.

[Drinfeld_91] ^  V. G. Drinfel'd, On quasitriangular Quasi-Hopf algebras and a group closely connected with $\operatorname {Gal} ({\bar {\mathbb {Q} }}/{\mathbb {Q} })$, Leningrad Math. J. 2 (1991) 829-860.