4. Let $M$ be the set of midpoints of all edges of a cube. Then the number of planes that pass through and only through three points in $M$ is ( ).
(A) 56
(B) 81
(C) 136
(D) 145
4. A.

Through three points in $M$, there are $\mathrm{C}_{12}^{3}=$ 220 planes (including duplicates), among which, planes passing through and only through four points in $M$ total $C_{4}^{3} \times(9+12)=84$; planes passing through six points total $\mathrm{C}_{6}^{3} \times 4=80$. Therefore, the number of planes passing through and only through three points in $M$ is $220-84-80=56$.