One can check that for a Riemann tensor $R_{abcd}$, using the standard definitions of the symmetry bracket "(...)" and the anti-symmetry bracket "[...]",
\begin{align} R_{a(bcd)}=0 \quad (\text{using}\ R_{abcd}=-R_{abdc}) \end{align} \begin{align} R_{a[bcd]}=0 \quad (\text{first Bianchi identity}) \end{align}
How is it possible that the same set of indices ($b, c, d$ above) are both symmetric and anti-symmetric at the same time?
