Abstract
Instead of attempting to prove that the general cubic surface contains 27 lines, I refer the reader to an excellent account in the treatise of Miller, Blichfeldt and Dickson [1916, pp. 343–344]. The early history of this famous arrangement of lines is described in Section 2. Here I am indebted to L. Kollros, who edited the collected works of Schläfli [1858, p. 216]. I make consistent use of Schläfli’s “epoch-making” notation, even though it has the disadvantage of specializing one of the 36 double sixes. A completely symmetrical notation, in which the number 27 arises as 33 instead of 12 + 15, was devised by Philip Hall [see Coxeter 1930, p. 396], improved by Frame [1938, p. 660] and perfected by Beniamino Segre [1942, p. 3; see also Coxeter 1974, p. 119].
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Coxeter, H.S.M. (1983). The Twenty-Seven Lines on the Cubic Surface. In: Gruber, P.M., Wills, J.M. (eds) Convexity and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5858-8_5
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