Models from the 19th Century used for Visualizing Optical Phenomena and Line Geometry

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The main focus of this paper is on models of quartic surfaces, especially so-called complex surfaces. These are special fourth-degree surfaces that Julius Plücker introduced in the 1860s for visualizing the local structure of a quadratic line complex. Plücker's complex surfaces turned out to be closely related to Kummer surfaces and both of these types of quartics are examples of caustic surfaces, which arise in geometrical optics. Indeed, Kummer surfaces represent a natural generalization of the wave surface, first introduced by Augustin Fresnel to explain double refraction in biaxial crystals.