3. Among the lines connecting the eight vertices of a square, the number of pairs of skew lines is ( ).
(A) 114
(B) 138
(C) 174
(D) 228
3. (C).

The vertex connections include 12 edges, 12 face diagonals, and 4 body diagonals. Skew lines can be categorized as follows:
(1) Edge to edge $\frac{12 \times 4}{2}=24$ pairs.
(2) Edge to face diagonal $12 \times 6=72$ pairs.
(3) Edge to body diagonal $12 \times 2=24$ pairs.
(4) Face diagonal to face diagonal $\frac{12 \times 5}{2}=30$ pairs.
(5) Face diagonal to body diagonal $12 \times 2=24$ pairs.
(G) Body diagonal to body diagonal (six at the center) 0 pairs.

Total: 174 pairs.