Tension polynomial \pol Gk of a graph $G$, evaluating the number of
nowhere-zero $\Bbb Z_k$-tensions in $G$, is the nontrivial divisor
of the chromatic polynomial $\chi_G(k)$ of $G$, because
$\chi_G(k)=k^{c(G)}\pol Gk$, where $c(G)$ denotes the number of
components of $G$. In this paper we present a new characterization
of these polynomials and show that \pol Gk can be presented as a sum
of some Ehrhart polynomials (evaluating the numbers of integral
vectors in multiples of integral polytopes). In a similar way we
introduce a new notion, integral tension polynomial \spol Gk, which
evaluates the number of nowhere-zero integral tensions in $G$ with
absolute values smaller than $k$. Furthermore we show that
$2^{r(G)}\pol Gk\geq\spol Gk\geq (r(G)+1)\pol Gk$ (where
$r(G)=|V(G)|-c(G)$) and $\pol G{k+1}\geq\pol Gk\cdot k/(k-1)$,\
$\spol G{k+1}\geq\spol Gk\cdot k/(k-1)$ for every $k>1$.
