Cayley surface

An algebraic ruled surface which is a translation surface with an $\infty^1$ translation net. Its equation in Cartesian coordinates is

$$x^3-6xy+6z=0.$$

The surface is named after A. Cayley [1], who considered it as a geometrical illustration of his investigations in the theory of pencils of binary quadratic forms.

References

[1]	A. Cayley, "A fourth memoir on quantics" , Collected mathematical papers , 2 , Cambridge Univ. Press (1889) pp. 513–526 (Philos. Trans. Royal Soc. London 148 (1858), 415–427)
[2]	V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)