Hi,
I have removed/replaced the hotlink,
There are no losses with both formulas. with sqrt(3)/6 the pixel count stays the same. with 1/PI the pixel count is slightly bigger.
sorry, I don't agree
same pixel counts doesn't mean some resolution/details,
e.g. the first complete pixel line in a spherical image will result after remapping to cube in just one single pixel,
and some informations/details in the middle of each cubeface will be lost, but...
Both formulas are viable.
...in practice - yes
best regards,
Klaus