Electric quadrupole transitions are revealed through the angular dependence of X-ray absorption spectra in a cubic crytal. Data collection was achieved at the iron K-edge in pyrite (FeS2) by using the angular moment method developed for X-ray Natural Circular Dichoism (XNCD) measurements. The natural linear dichroism (XNLD) was found to be around 0.5% of the edge jump. Experimental results are compared with monelectronic and multilectronic calculations. Calculations allow to quantitatively determine the proportion of quadrupolar transitions in the pre-edge structure and the anisotropy is explained in terms of structural and electronic parameters.