Surfaces54 of 113
Clebsch diagonal cubic
Alfred Clebsch, 1871
Every smooth cubic surface contains exactly 27 straight lines. On most they are partly imaginary; on Clebsch’s diagonal surface all 27 are real, and Klein had a plaster model of it made with the lines drawn on.
81(x³+y³+z³) − 189(x²y+x²z+y²x+y²z+z²x+z²y) + 54xyz + 126(xy+xz+yz) − 9(x²+y²+z²) − 9(x+y+z) + 1 = 0
On mathcurve.com as Cubique de Clebsch