6. In space, there are 4 non-coplanar fixed points. The number of parallelepipeds that can be formed with these 4 points as vertices is ( ).
(A) 20
(B) 32
(C) 25
(D) 29
6. (D).
Each parallelepiped is uniquely determined by the designated 1 vertex and 3 median planes (each of these median planes is equidistant from all vertices of the parallelepiped). For any given 4 non-coplanar points, there exist 7 planes equidistant to these 4 points. Choosing any 3 out of these 7, there are $\mathrm{C}_{7}^{3}=35$ ways. However, now we need 3 planes that intersect at one point (the center of the parallelepiped), so we must exclude the groups of three planes that are parallel to the same line, and there are 6 such groups. Therefore, the total number of parallelepipeds that can be determined is 29.