Let $U$ be the set of unipotent upper triangular matrices and $B$ the upper triangular matrices of $GL_3$. How could I describe $GL_3/U$ ? Using coordinates, in a projective or an affine space.

For example, I already know the identification of $SL_2/U$ with $\mathbb{A}^2 \setminus (0,0)$ and the identification of $SL_2/B$ with $\mathbb{P}^1$ ($B,U$ the standard Borel of $SL_2$ and its unipotent radical).

Thank you.