Cubic surfaces

A cubic surface in real 3-dimensional space is the set of zeros of a polynomial of degree 3 in three variables. Considering the corresponding "complex projective" surface yields a classification of double points. There are conic double points, biplanar double points B3, B4, B5, B6, and three kinds of uniplanar double points. Explanations can be found in Schilling's catalogue, and in chapter 2 of the commentary edited by Fischer, cf. References (RE).

Img(72) Ruled surface of 3. orderImg(73) Ruled surface of 3. order
Img(74) Ruled surfaces of 3. orderImg(75) Ruled surface of 3. order
Img(80) Cone of third orderImg(81) Cone of third order
Img(82) Cone of third orderImg(83) Cone of third order
Img(84) Cone of third orderImg(85) Cone of third order
Img(86) Cone of third orderImg(135) Clebsch's diagonal surface
Img(136) Cubic surface with 4 real conic double pointsImg(137) Affine form of the cubic surface136
Img(138) Affine form of the cubic surface 136Img(139) Affine form of the cubic surface 136
Img(140) Affine form of the cubic surface 136Img(141) Cubic surface with 3 real conic double points
Img(142) Cubic surface with 3 real conic double pointsImg(143) Cubic surface with 3 real biplanar double points
Img(144) Cubic surface with with a biplanar double pointImg(145) Cubic surface with a biplanr double point
Img(146) Cubic surface with with a biplanar and 2 real conic double pointsImg(147) Cubic surface with a biplanar double point
Img(148) Cubic surface with a conic and a biplanar double pointImg(149) Cubic surface with a real conic and a biplanar double point
Img(150) Cubic surface with 4 real double points