# 6j symbol The $6j$ symbol is written as$\left\{\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right\}.$It has the symmetry of column permutations and swapping the first and second rows of any two columns simultaneously, i.e.,$\left\{\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right\}=\left\{\begin{array}{lll}2 & 1 & 3 \\ 5 & 4 & 6\end{array}\right\}=\left\{\begin{array}{lll}3 & 2 & 1 \\ 6 & 5 & 4\end{array}\right\}=\cdots,$and$\left\{\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right\}=\left\{\begin{array}{lll}4 & 5 & 3 \\ 1 & 2 & 6\end{array}\right\}=\cdots.$ It can be presented by a tetrahedron. The edges on opposite sides are in the same column.