Essential virtual pairs:

$S: BQ^3_{6} \quad U = ((1 2) , (2 3) , (1 3)) \quad D = ((1 2 3) , (1 2 3) , (1 2 3))$\hfil\break
$T: BQ^3_{7} \quad U = ((1 2 3) , (1 2 3) , (1 2 3)) \quad D = ((1 3 2) , (1 3 2) , (1 3 2))$\hfil\break

$S: BQ^3_{6} \quad U = ((1 2) , (2 3) , (1 3)) \quad D = ((1 2 3) , (1 2 3) , (1 2 3))$\hfil\break
$T: Q^3_{1} \quad U = \iota \quad D = \iota$\hfil\break

$S: Q^3_{3} \quad U = ((2 3) , (1 3) , (1 2)) \quad D = \iota$\hfil\break
$T: BQ^3_{7} \quad U = ((1 2 3) , (1 2 3) , (1 2 3)) \quad D = ((1 3 2) , (1 3 2) , (1 3 2))$\hfil\break