In the representation theory of $SU_2$ a big role is played by so-called $6-j$symbols

$$\begin{bmatrix}

a & b & c\\

d & e & f\\

\end{bmatrix}.$$

There definition can be found here.

Among there symmetries the most mysterious is a famous *Regge symmetry:*

$$

\begin{bmatrix}

a & b & c\\

d & e & f\\

\end{bmatrix}=

\begin{bmatrix}

a & s-b & s-c\\

d & s-e & s-f\\

\end{bmatrix},

$$

where $s=\frac{b+c+e+f}{2}.$

What is the physical significance of this symmetry? Are there any currently known applications of it?