Some functions of points in projective spaces (Q1373243)

In 1995, the author proved a conjecture of B. Gruenbaum which states that in every \(n\)-polygon \(P\) (\(n \geq 5\)) of the real projective plane the intersection of certain diagonals of \(P\) defines a new \(n\)-polygon \(\delta (P)\), such that the product of the cross-ratios on the diagonals of \(P\) equals the product of the corresponding cross-ratios on the diagonals of \(\delta (P)\) [ibid. 60, 145-151 (1996; Zbl 0848.51012)]. In the paper under review the author generalizes this result to \(n\)-polygons (with \(n \geq d+2\)) of the real \(d\)-dimensional projective space.