It is known that contracting over the vector indices of two Pauli matrix can be simplified to a bunch of delta functions. This is done via Fierz formula $$\delta_{ab}\sigma^a_{ij}\sigma^b_{kl}=\delta_{ij}\delta_{kl}-2\epsilon_{ik}\epsilon_{jl}=2\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl}$$ Here, $a,b,c=1,2,3$ are vector indices, and $i,j,k,l=1,2$ are spinor indices. Repeated indices are summed over.
However, I would like to know whether there is a similar formula for $$\epsilon_{abc}\sigma^a_{ij}\sigma^b_{kl}\sigma^c_{pq}$$ If so, what is it? Many thanks!