We prove that mirror nonsingular configurations of m points and n lines in ℝP³ exist only for m ≤ 3, n ≡ 0 or 1 (mod 4) and for m = 0 or 1 (mod 4), n ≡ 0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov's well-known result saying that if a nonsingular surface of degree four in ℝP³ is noncontractible and has M ≥ 5 components, then it is nonmirror. For the cases M = 5, 6, 7, and 8, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of M -1 points and a line. Our proof covers the remaining cases M = 9, 10.