Given the following polyhedron: All the $n\times n$ matrices $\boldsymbol{X}$ with elements $x_{ij}\in(0,1)$ such that $$\boldsymbol{X}\cdot\boldsymbol{1}=\boldsymbol{r}, \boldsymbol{1}^T\boldsymbol{X}=\boldsymbol{c}^T$$

For some given vectors $\boldsymbol{r}$ and $\boldsymbol{c}$.

Can I calculate the volume of this polyhedron? Can I calculate it's surface?