Klein cubic threefold

In algebraic geometry, the Klein cubic threefold is the non-singular cubic threefold in 4-dimensional projective space given by the equation

studied by Klein (1879). Its automorphism group is the group PSL₂(11) of order 660 (Adler 1978). It is unirational but not a rational variety. Gross & Popescu (2001) showed that it is birational to the moduli space of (1,11)-polarized abelian surfaces.