Clebsch Surface: 27 Lines on a Cubic

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This is a model of a Clebsch Surface. Although the surface is curved, it contains exactly 27 straight lines. It is a classic theorem in algebraic geometry that a general surface defined by degree-3 polynomial in three variables will contain 27 lines. That is, while the surface itself is probably curved, there are 27 places where it "straightens out" into a line. The problem, though, is that this theorem only works if we include complex numbers (like the square root of -1) and the plane at infinity; thus, usually some of the lines are invisible to us in the real world. However, in the Clebsch Surface (studied by Felix Klein and Alfred Clebsch in the 1870s), all 27 of the lines appear in the real numbers. The lines are marked in the attached image.