Every non-singular complex projective cubic surface has $27$ lines. Many such surfaces contain points where three lines intersect (called Eckardt points). There are even surfaces with many Eckardt points, like the Fermat cubic, which has $18$. Is there any such non-singular complex projective cubic surface where four, five, or six lines intersect at a point? (I asked this on Math StackExchange as well.)

Every non-singular complex projective cubic surface has $27$ lines. Many such surfaces contain points where three lines intersect (called Eckardt points). There are even surfaces with many Eckardt points, like the Fermat cubic, which has $18$. Is there any such non-singular complex projective cubic surface where four, five, or six lines intersect at a point?

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Every non-singular complex projective cubic surface has $27$ lines. Many such surfaces contain points where three lines intersect (called Eckardt points). There are even surfaces with $18$ Eckardt points, like the Fermat cubic. Is there any such non-singular complex projective cubic surface where four, five, or six lines intersect at a point? (I asked this on Math StackExchange as well.)

Every non-singular complex projective cubic surface has $27$ lines. Many such surfaces contain points where three lines intersect (called Eckardt points). There are even surfaces with many Eckardt points, like the Fermat cubic, which has $18$. Is there any such non-singular complex projective cubic surface where four, five, or six lines intersect at a point? (I asked this on Math StackExchange as well.)