AHSME 1995 Problem 30

A large cube is formed by stacking 27 unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is $\mathrm{(A) \ 16 } \mathrm{(B) \ 17 } \mathrm{(C) \ 18 } \mathrm{(D) \ 19 } \mathrm{(E) \ 20 }$