An experiment populating low/medium-spin states in156 Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148 Nd( 12 C,4n) reaction and the Gammasphere array was utilized to detect the emitted γ rays. B(E2)/B(E1) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. In addition, several other negative-parity structures were observed to higher spin and two new sequences were established.