Central topic of this work is the analytical investigation to determine the mechanical properties of unit cells, which are used for lattice structures in additive manufacturing. This production technology is becoming increasingly important in the production of optimized and load-oriented components. For example, the energy absorption capacity of crash components can be improved enormously by the targeted use of metal foams. The mechanical behavior of lattice structures can be characterized by an analytical consideration of the unit cell. This mechanical behavior subsequently significantly influences the optimization of the components and thus the final design. In this work, a three-dimensional unit cell with octahedral basic shape is investigated. The developed analytical model should be checked for plausibility by a numerical simulation. Finally, the investigated cell is compared with other geometric unit cells to determine the respective performance via the Ashby approach.