An updated analysis using about 1.5 million events recorded at √s = Mz with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in script O(α2s) including the event orientation. A combined fit of αs and of the renormalization scale xμ in script O(α2s) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is αs(M2z) = 0.1174±0.0026. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is αs(M2z) = 0.1180 ± 0.0006(exp.) ± 0.0013(hadr.) ± 0.0008(scale) ± 0.0007(mass). Further studies include an αs determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and script O(α2s) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Padé approximants. Average αs values derived from the different approaches are in good agreement.