If $({\mathscr{C}},m)$ is a weighted integral ${\mathbb{R}}$-affine polyhedral complex of pure dimension $n$, then we get a supercurrent $\delta_{({\mathscr{C}},m)}\in D_{n,n}(N_{\mathbb{R}})$ by setting $\delta_{({\mathscr{C}},m)}(\eta)=\int_{({\mathscr{C}},m)}\eta$ for any $\eta\in A_{c}^{n,n}(N_{\mathbb{R}})$.