[en] Negative-parity bands in the vicinity of ¹⁵⁶Gd and ¹⁶⁰Yb have been suggested as candidates for the rotation of tetrahedral nuclei. We report the observation of the odd and even-spin members of the lowest energy negative-parity bands in ¹⁶⁰Yb and ¹⁵⁴Gd. The properties of these bands are similar to the proposed tetrahedral band of ¹⁵⁶Gd and its even-spin partner. Band-mixing calculations are performed and absolute and relative quadrupole moments deduced for ¹⁶⁰Yb and ¹⁵⁴Gd. The values are inconsistent with zero, as required for tetrahedral shape, and the bands are interpreted as octupole vibrational bands. The failure to observe the in-band E2 transitions of the bands at low spins can be understood using the measured B(E1) and B(E2) values.