On an even dimensional planet there would be N/2 longitudes that range from 0 to 360 and N/2-1 latitudes that range from 0 to 90. Chose one special plane of rotation -- all of the latitudes are relative to it.
On odd dimensional planets add one more longitude relative to the axis that ranges from 0 to 180.
According to Wikipedia, the usual scheme for N dimensional polar coordinates is one 360 degree longitude and the rest 0 to 180 degrees. It's more convenient for converting to-from Cartesian coordinates.