Isomerism is shown by \([Co(NH_3)_3(NO_2)_3]\) is

Facial and meridional

The isomerism shown by \([Co(NH_3)_3(NO_2)_3]\) is facial and meridional.

Facial and meridional isomerism is a type of geometrical isomerism that occurs in octahedral complexes. In an octahedral complex, the six ligands are arranged around the central metal atom in two groups of three. If the three ligands of the same type are arranged on the same face of the octahedron, the isomer is called facial. If the three ligands of the same type are arranged in a triangular fashion around the octahedron, the isomer is called meridional.

\([Co(NH_3)_3(NO_2)_3]\) can exist as both a facial and a meridional isomer. The facial isomer has the three NH3 ligands on one face of the octahedron, and the three \(NO_2\) ligands on the other face. The meridional isomer has one \(NH_3\) ligand on each of the three faces of the octahedron, and the three \(NO_2\) ligands are arranged in a triangular fashion around the octahedron.

Here are the structural diagrams of the facial and meridional isomers of \([Co(NH_3)_3(NO_2)_3]\):