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The Cayley cubic

Up to projective isomorphism there is exactly one surface of degree three (cubic) with µ(3)=4 nodes. This surface is called Cayley cubic and satisfies the following equation:

4(x^3+y^3+z^3+w^3)-(x+y+z+w)^3=0

[120x120 pixel image of Cayley-cubic] 28K

The Cayley cubic is invariant under the symmetry group of the tetrahedron S4 and contains exactly nine lines: six lines connecting the four nodes pairwise and another three coplanar lines.

The classification of singular cubic surfaces is due to the mathematicians Artur Cayley and Ludwig Schläfli.

Stephan Endraß
Last update: Thursday, 06-Feb-2003 08:52:20 CET

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