High-spin states in Lu164 were populated in the Sb121(Ca48,5n) reaction at 215 MeV and γ-ray coincidences were measured with the Gammasphere spectrometer. Through this experiment the eight known triaxial superdeformed bands in Lu164 could be confirmed. Some of these bands were extended to higher as well as to lower spins. Evidence is reported for the first time for weak ΔI=1,E1 transitions linking TSD3 and TSD1. This observation may imply coupling to octupole vibrational degrees of freedom. The decay mechanism is different from the one observed in the neighboring even-N isotopes, which exhibit wobbling excitations built on the πi13/2 structure with E2(M1),ΔI=1 interband decay. An additional sequence decaying at high spin into TSD1 was observed up to Iπ=(50-). This band has a constant dynamic moment of inertia of ∼70 2MeV-1 and an alignment that is ∼2 larger than that found for TSD1. A revision of the assumed spin-parity-assignment of TSD2 is based on the observed decay-out to normal-deformed structures. The parity and signature quantum numbers of TSD2 are now firmly assigned as (π,α)=(+,0), in disagreement with the former assignment of (π,α)=(-,1), which was based on the assumption that TSD2 is the signature partner of TSD1. TSD1 and TSD2 show an alignment gain at ω∼0.67 and 0.60 MeV, respectively. In TSD1 the involvement of the j15/2 neutron orbital is suggested to be responsible for the high-frequency crossing
