Twelve general position points always form three intersecting tetrahedra

AbstractThis note answers affirmatively the following question which appeared in a list of problems [3] generated by a July, 1977 Discrete Geometry conference at Oberwolfach: “Given 12 points in general position in space, can one always put them into 3 sets of 4 each so that the 3 tetrahedra have an interior point in common?” Related conjectures are considered