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The Clebsch is a cubic surface given by the following two equations:
x0^3+x1^3+x2^3+x3^3+x4^3=0 x0+x1+x2+x3+x4=0Every smooth cubic surface contains 27 complex lines. In the case of the Clebsch diagonal surface, all 27 lines are real. These 27 lines are drawn on the model. There are 10 points on the surface where 3 of the 27 lines meet, called Eckardt points. The Clebsch diagonal surface is the unique cubic surface containing 10 such points.
Cayetano Ramírez López .
Department of Mathematics, University of Groningen