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

${\displaystyle \displaystyle x_{0}+x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=0}$

${\displaystyle \displaystyle x_{0}^{3}+x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{3}+x_{5}^{3}=0.}$

The intersection of the Segre cubic with any hyperplane x_i = 0 is the Clebsch cubic surface. Its intersection with any hyperplane x_i = x_j is Cayley's nodal cubic surface. Its dual is the Igusa quartic 3-fold in P⁴. Its Hessian is the Barth–Nieto quintic. A cubic hypersurface in P⁴ has at most 10 nodes, and up to isomorphism the Segre cubic is the unique one with 10 nodes. 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).^[1]