Fresnel's Elasticity Surface

A Quartic Surface given by

$$r=\sqrt{a^2x^2+b^2y^2+c^2z^2},$$

where

$$r^2\equiv x'^2+y'^2+z'^2,$$

also known as Fresnel's Wave Surface. It was introduced by Fresnel in his studies of crystal optics.

References

Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, p. 16, 1986.

Fischer, G. (Ed.). Plates 38-39 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 38-39, 1986.

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 304, 1993.