I was thinking, I know that the earth has to be distorted when projected on a flat map because the space nearer the poles of the earth does not have a much circumference but is expending the same amount of flat space. Could you not do an accurate flat projection by making the earth a diamond, or a diamond with curved sides? Or some possible combination of 'rotated' tetragon? I hope this is the appropriate forum. Either way, thanks a lot!