The surface and emission images of a metal field's electron cathode in the form of a tip are simulated. The surface structure is calculated in the thin-shell and broken-bond (local-environment) models for the perfect crystal lattice. The cathode shape and macroscopic electric field are represented by the sphere-on-cone model. The amplification of a local electric field is the adjustable parameter of the model. The method of determination of the emitter tip's crystal faces based on the analysis of the surface atoms' environment geometry is proposed. It is shown that it is enough to restrict the consideration of geometric environment by the fifth order of the nearest neighbors for the emitter radius of 100-1000 lattice parameters (31.6-316 nm for the tungsten). The crystallographic model of work function anisotropy in the broken-bond approach is used: the local work function's value is set in accordance with Miller indices of the face containing this area. The model adequacy is corroborated by the comparison of current-voltage characteristics and emission images with the data of the natural experiment.