Given $n$ vectors $v_1, \ldots, v_n$ in $\mathbb{R}^n$ of course we all know at least one measure for their relative configuration: $|v_1 \wedge\ldots \wedge v_n|$. Now suppose one were given $n$ pairs $(e_1,f_1), \ldots, (e_n,f_n)$ in $\mathbb{R}^{2n}$---then what could be a meaningful measure for their relative configuration? Suppose moreover we require this measure to be $geometric$ ie. having fixed, say a full rank lattice $\Gamma$ in $\mathbb{R}^{2n}$ what could be a meaningful measure for the relative configuration of n 2-planes $\pi_1, \ldots, \pi_n$ in $\mathbb{R}^{2n}$?