This study is based on a series of nine direct numerical simulations of homogeneous turbulence, in which the rotation ratio f /S of Coriolis parameter to shear rate is varied. The presence of rotation stabilizes the flow, except for a narrow range of rotation ratios 0,f /S,1. The main mechanism for the flow's destabilization is an increased turbulence production due to increased anisotropy. Reynolds stress and the dissipation rate anisotropy tensors have been evaluated and provide a reference for newly defined anisotropy measures. Wavelet-based directional energies capture the properties of velocity gradients. The intermittency of the flow in different directions is quantified with scale-dependent directional flatness. Scale-dependent helicity probability distribution functions allow one to statistically characterize the geometry of the motion at different scales. Small scales are found locally to be predominantly helical, while large scales are not since they tend to two-dimensionalization for cases with growing turbulent kinetic energy. Joint probability distribution functions show that the signs of velocity helicity and vorticity helicity are strongly correlated. This indicates that vorticity helicity tends to diminish velocity helicity. © 2010 American Institute of Physics.