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nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sun Aug 03, 2014 10:16 pm    Post subject: Cayley Cubic (deg 3)

Hi,
Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant under the tetrahedral group and contains exactly nine lines, six of which connect the four nodes pairwise and the other three of which are coplanar (Endraß).
K3DSurf code:
 Code: Name: Cayley_2 F(): (x^2 + y ^2 - x^2 *z + y ^2 *z + z ^2 -1) [x]: -4 , 4 [y]: -4 , 4 [z]: -4 , 4 Cnd:   (sqrt(x^2  + y ^2 + z ^2)) < 4 ; Name: Cayley_1 F():  -5*(x*x*y + x*x*z + y*y*x + y*y*z + z*z*y + z*z*x)   +2*(x*y + x*z + y*z) [x]: -1 , 1 [y]: -1 , 1 [z]: -1 , 1 Cnd:   (sqrt(x^2  + y ^2 + z ^2)) < 1 ;

Cayley_1
by taha_ab, on Flickr
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Cheers,
Abderrahman
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