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Clebsch Surface: 27 Lines on a Cubic – 3D printable model from Thingiverse Thingiverse

Clebsch Surface: 27 Lines on a Cubic

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This is a model of a [Clebsch Surface](https://en.wikipedia.org/wiki/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* number
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