Minimal surface stretched over four points

Question

Let $x_0, \ldots, x_3 \in \mathbb{R}^3$. Let $C$ be a pathwise affine curve connecting these points in order $x_0 \to x_1 \to x_2 \to x_3 \to x_0$. (That is, $C$ consists of four segments that connect $x_i$ to $x_{i+1}$ with $x_4 = x_0$). I would like to know if there is an explicit formula for the minimal surface bounded by $C$ (or, at least, a formula for the area of this surface).