The manganate and permanganate ions are tetrahedral, due to:

• The $\mathrm{\pi }$ bonding involves overlap of p-orbitals of oxygen with p-orbitals of manganese.
• Manganate and permanganate ions are tetrahedral because overlapping of p-orbitals of oxygen with d-orbitals of manganese. Manganate- $\mathrm{\pi }$bonds are of $\mathrm{\pi }$d-$\mathrm{\pi }$p type. 
• In permanganate ( MnO₄^-),

                        $\mathrm{\pi }- \mathrm{bonds} \mathrm{are} \mathrm{of} \mathrm{p\pi }-\mathrm{d\pi } \mathrm{type}.$

• In manganate (${\mathrm{MnO}}_4^{-2}$)

                  $\mathrm{\pi }- \mathrm{bonds} \mathrm{are} \mathrm{of} \mathrm{p\pi }-\mathrm{d\pi } \mathrm{type}.$