Segre surface

In algebraic geometry, a Segre surface, studied by Corrado Segre (1884) and Beniamino Segre (1951), is an intersection of two quadrics in 4-dimensional projective space. They are rational surfaces isomorphic to a projective plane blown up in 5 points with no 3 on a line, and are del Pezzo surfaces of degree 4, and have 16 rational lines. The term "Segre surface" is also occasionally used for various other surfaces, such as a quadric in 3-dimensional projective space, or the hypersurface

$x_1{x}_2{x}_3+x_2{x}_3{x}_4+x_3{x}_4{x}_5+x_4{x}_5{x}_1+x_5{x}_1{x}_2=0.$