Clebsch Surface: 27 Lines on a Cubic

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This is a model of a surface known as the Clebsch Surface. Despite its curved shape, it boasts exactly 27 straight lines. A fundamental theorem in algebraic geometry states that any general surface defined by a degree-3 polynomial in three variables will contain 27 such lines. While the surface itself may be curved, there are indeed 27 specific points where it temporarily "straightens out" into a line. However, this theorem only applies when we include complex numbers and the plane at infinity; consequently, many of these lines often remain invisible to us in the real world. In striking contrast, the Clebsch Surface studied by Felix Klein and Alfred Clebsch in the 1870s features all 27 lines within the realm of real numbers. The surface's lines are clearly marked in the accompanying image.