Check my work: cube side lenght

A cube has edges parallel to the axes. One corner is at A = (5,1,2) and the corner at the other end of the longest diagonal through A is B = (12,7,4). Find the coordinates of the other vertices on the cube.

This should be a dumb-easy question. I Used the distance formula to find the distance between the two as a diagonal.: sqrt[(12-5)^2+(7-1)^2+(4-2)^2] = 9.473.

Since the diagonal forms a 45-45-90 triangle, I know that the ratio of the length of the sides is x:x:x*sqrt(2). So, I divide the length I calculated before by sqrt(2). The answer I get is 6.69, which is not a whole number. However, the answers have all whole numbers. What am I doing wrong?