Using Sloan Digital Sky Survey Data Release 5 , we have investigated the intrinsic axis ratio distribution ( ARD ) for early-type galaxies .
We have constructed a volume-limited sample of 3,922 visually-inspected early-type galaxies at 0.05 \leq z \leq 0.06 carefully considering sampling biases caused by the galaxy isophotal size and luminosity .
We attempt to de-project the observed ARD into three-dimensional types ( oblate , prolate , and triaxial ) , which are classified in terms of triaxiality .
We confirm that no linear combination of randomly -distributed axis ratios of the three types can reproduce the observed ARD .
However , using Gaussian intrinsic distributions , we have found reasonable fits to the data with preferred mean axis ratios for oblate , prolate , and triaxial ( triaxials in two axis ratios ) , \mu _ { o } = 0.44 , \mu _ { p } = 0.72 , \mu _ { t, \beta } = 0.92 , \mu _ { t, \gamma } = 0.78 where the fractions of oblate , prolate and triaxial types are \textrm { O:P:T } = 0.29 ^ { \pm 0.09 } : 0.26 ^ { \pm 0.11 } : 0.45 ^ { \pm 0.13 } .
We have also found that the luminous sample ( -23.3 < M _ { r } \leq - 21.2 ) tends to have more triaxials than the less luminous ( -21.2 < M _ { r } < -19.3 ) sample does .
Oblate is relatively more abundant among the less luminous galaxies .
Interestingly , the preferences of axis ratios for triaxial types in the two luminosity classes are remarkably similar .
We have not found any significant influence of the local galaxy number density on ARD .
We show that the results can be seriously affected by the details in the data selection and type classification scheme .
Caveats and implications on galaxy formation are discussed .