The aim of this paper is to introduce and characterize, both experimentally and numerically, three classes of non-traditional 3D infill patterns at three scales as an alternative to classical 2D infill patterns in the context of additive manufacturing and structural applications. The investigated 3D infill patterns are biologically inspired and include Gyroid, Schwarz D and Schwarz P. Their selection was based on their beneficial mechanical properties, such as double curvature. They are not only known from nature but also emerge from numerical topology optimization. A classical 2D hexagonal pattern has been used as a reference. The mechanical performance of 14 cylindrical specimens in compression is quantitatively related to stiffness, peak load and weight. Digital image correlation provides accurate full-field deformation measurements and insights into periodic features of the surface strain field. The associated variability, which is inherent to the production and testing process, has been evaluated for 3 identical Gyroid specimens. The nonlinear material model for the preliminary FEM analysis is based on tensile test specimens with 3 different slicing strategies. The 3D infill patterns are generally useful when the extrusion orientation cannot be aligned with the build orientation and the principal stress field, i.e., in case of generative design, such as the presented branching structure, or any complex shape and boundary condition.