Tritangent Planes
A tritangent plane is a plane which intersects the surface in three lines.
The picture above shows three tritangent planes.
A nondegenerate cubic surface has exactly 45 tritangent planes.
Tritangent planes come in two types:
Either the three lines are concurrent in a point or not.
In the picture, the topmost tritangent plane has three concurrent lines.
The other two tritangent planes have their lines form triangles each.
Notice that the three planes are parallel. This means that they intersect at infinity in a line.
We cannot show this line in an affine picture,
but we can imagine that there is a line "far away" where the three planes come together.
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On 4 Jun 2017, 11:23.