In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 (or sometimes 5) dimensional projective space, studied by Corrado Segre (1887).
The Segre cubic is the set of points (x0:x1:x2:x3:x4:x5) of P5 satisfying the equations The intersection of the Segre cubic with any hyperplane xi = 0 is the Clebsch cubic surface.
Its intersection with any hyperplane xi = xj is Cayley's nodal cubic surface.
Its nodes are the points conjugate to (1:1:1:−1:−1:−1) under permutations of coordinates.
The Segre cubic is rational and furthermore birationally equivalent to a compactification of the Siegel modular variety A2(2).