6 space has 4 non-coplanar fixed points. The number of parallelepipeds 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 $C_{7}^{3}=35$ ways. However, now we need 3 planes that intersect at one point (the center of the parallelepiped), so we should exclude those sets of three planes that are parallel to the same line, and there are 6 such sets. Therefore, the total number of parallelepipeds that can be determined is 29.