(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 3 points in $M$ is ( ).
(A) 56
(B) 81
(C) 136
(D) 145
(4) A Hint: The number of planes through 3 points in $M$ is $\mathrm{C}_{12}^{3}=220$ (including duplicates), among which the planes passing through and only through 4 points in $M$ are 
$$
\mathrm{C}_{4}^{3} \times(9+12)=84 \text { (planes). }
$$

The planes passing through 6 points in $M$ are $\mathrm{C}_{6}^{3} \times 4=80$ (planes); therefore, the planes passing through and only through 3 points in $M$ are $220-84-80=56$ (planes). Hence, the answer is A.