Some remarks on the theorem of Möbius (Q1339796)

The author refers to the following theorem of Möbius (on pairs of tetrahedra) as it is quoted in \textit{H. S. M. Coxeter}'s book `Introduction to geometry' (1961; Zbl 0095.345): ``If the four vertices of one tetrahedron lie respectively in the four face planes of another, while three vertices of the second lie in three face planes of the first, then the remaining vertex of the second lies in the remaining face plane of the first''. He gives two counterexamples. A corrected version of the theorem (presuming both tetrahedra to be nondegenerate) is stated and proved.