We have synthesized three different shapes of $$\hbox{Co}_{3}\hbox{O}_{4}$$
Co
3
O
4
nanoparticles to investigate the relationships between the surface Co$$^{2+}$$
2
+
and Co$$^{3+}$$
3
+
bonding quantified by exploiting the known exposed surface planes, terminations, and coordiations of $$\hbox{Co}_{3}\hbox{O}_{4}$$
Co
3
O
4
nanoparticle spheres, cubes and plates. Subsequently this information is related to the unusual behaviour observed in the magnetism. The competition of exchange interactions at the surface provides the mechanism for different behaviours in the shapes. The cubes display weakened antiferromagnetic interactions in the form of a spin-flop that occurs at the surface, while the plates show distinct ferromagnetic behaviour due to the strong competition between the interactions. We elucidate the spin properties which are highly sensitive to bonding and crystal field environments. This work provides a new window into the mechanisms behind surface magnetism.