Graves triads,Möbius pairs,and related matrices

A Graves triad is a cyclic triad of triangles, each circumscribing the next, forming a Pappus configuration. If two of the triangles are in perspective, then so are the other two pairs. In a non-cyclic triad of such circumscribing triangles, if two pairs are in perspective, then so is the third pair. These results correspond to certain properties of 3×3 zero-diagonal matrices. There is also an analogous result for Möbius pairs of mutually circumscribing tetrahedra and 4×4 zero-diagonal matrices.