We present direct experimental evidence of the formation of a superstructure on the (111) surface of a magnetite, Fe3O4 single crystal. The superstructure, which has a periodicity of 42 A and three-fold symmetry, has been observed by means of STM and LEED. Under the correct conditions of oxygen pressure and sample anneal temperature, the superstructure is reproducibly formed throughout most of the sample surface. Clear atomic resolution within the superstructure has been achieved. The characteristics of the superstructure, including its dependency on the tunnel bias voltage and its atomic-scale periodicity, suggest that it is an electronic effect rather than a mosaic of several iron oxide phases. We explain the results in terms of the formation of giant static polarons, although we notice that other types of electron-lattice instabilities such as charge density wave may offer possible explanations. Polarons with dimensions of many interatomic distances in three-dimensional systems are unlikely to exist but the situation for two- and one-dimensional cases is predicted to be different. We suggest three possible scenarios of instability linking the electron band structure and lattice distortions in magnetite: either resulting from reallocation of Fe2+ and Fe3+ valence states between octahedral sites or, alternatively, from reallocation between octahedral and tetrahedral sites.