  This article gives a description of the diagonal $GL_3$-orbits on the
quadruple projective variety $(\mathbb P^2)^4$. We give explicit
representatives of orbits, and describe the closure relations of orbits. A
distinguished feature of our setting is that it is the simplest case where
$\mathrm{diag}(GL_n)$ has infinitely many orbits but has an open orbit in the
multiple projective space $(\mathbb P^{n-1})^m$.
