The Twenty-Seven Lines on the Cubic Surface

摘要: Instead of attempting to prove that the general cubic surface contains 27 lines, I refer reader an excellent account in treatise Miller, Blichfeldt and Dickson [1916, pp. 343–344]. The early history this famous arrangement lines is described Section 2. Here am indebted L. Kollros, who edited collected works Schlafli [1858, p. 216]. make consistent use Schlafli’s “epoch-making” notation, even though it has disadvantage specializing one 36 double sixes. A completely symmetrical which number arises as 33 instead 12 + 15, was devised by Philip Hall [see Coxeter 1930, 396], improved Frame [1938, 660] perfected Beniamino Segre [1942, 3; see also 1974, 119].