Large scale calculations in a five-dimensional space of deformation parameters allow us to investigate the influence of quadrupole and hexadecapole non-axialities on the spontaneous fission life time estimates of nuclei. The macroscopic--microscopic method gives the total energy surfaces using the newest Lublin-Strasbourg Drop (LSD) macroscopic energy. The microscopic part is based on the single particle energy spectra of the Woods-Saxon single particle potential with the universal set of parameters in five-dimensional space of deformation parameters for each of about 200 even--even isotopes. Our aim is to obtain the total energy surfaces in the multidimensional space of deformation parameters paying special attention to non-axial quadrupole and hexadecapole parameters \alpha _2,2, \alpha _4,2, \alpha _4,4 and to compare them with the total energy surfaces obtained in the axially symmetric space \alpha _2,0, \alpha _4,0, \alpha _6,0, \alpha _8,0, \alpha _10,0 for the region of Cf-Ds and heavier nuclei.

PACS numbers: 21.60.--n