  In this note we prove an explicit formula for the lower semicontinuous
envelope of some functionals defined on real polyhedral chains. More precisely,
denoting by $H \colon \mathbb{R} \to \left[ 0,\infty \right)$ an even,
subadditive, and lower semicontinuous function with $H(0)=0$, and by $\Phi_H$
the functional induced by $H$ on polyhedral $m$-chains, namely \[ \Phi_{H}(P)
:= \sum_{i=1}^{N} H(\theta_{i}) \mathcal{H}^{m}(\sigma_{i}), \quad\mbox{for
every }P=\sum_{i=1}^{N} \theta_{i} [[ \sigma_{i} ]]
\in\mathbf{P}_m(\mathbb{R}^n), \] we prove that the lower semicontinuous
envelope of $\Phi_H$ coincides on rectifiable $m$-currents with the $H$-mass \[
\mathbb{M}_{H}(R) := \int_E H(\theta(x)) \, d\mathcal{H}^m(x) \quad \mbox{ for
every } R= [[ E,\tau,\theta ]] \in \mathbf{R}_{m}(\mathbb{R}^{n}). \]
