a 3 x 3 x 3 'parent' cube (like in a Rubik cube).

Assign unique values from 1 to 20 to the letters AT such that the sum of each pair of diametrically opposite cubes is to be the same as all others while the sum of each set of edge cubes may not differ from that of any other set by more than one.
Eg, diagonals: A + Q = N + E = C + O ...(etc) and edge cubes: A + B + C = C + E + H = F + G + H ...etc, or (A + B + C) ±1 = C + E + H = F + G + H ....(etc)Note: The problem's development and my solution used a spreadsheet; as such a wellconstructed sheet could enable a solution. Although this problem may lend itself to a programmed solution I would appreciate seeing attempts of a more manual basis within the first 2448 hrs.