21.1.7 Given 4 non-coplanar points in space, how many different parallelepipeds can be formed with these points as vertices?
Each parallelepiped is uniquely determined by the specified 1 vertex and 3 median planes (each of these median planes is equidistant from all vertices of the parallelepiped). For a given set of 4 points, there exist 7 planes equidistant to these 4 points. Choosing any 3 from these 7, and excluding those sets of three planes that are parallel to a single line (since the 3 chosen planes should intersect at a point, which is the center of the parallelepiped), there are $\mathrm{C}_{4}^{2}=6$ such sets, so the total number of parallelepipeds determined is $\mathrm{C}_{7}^{3}-6=29$.