Let $X$ be a complete $\Q$-factorial toric variety of dimension $n$ and
$\del$ the fan in a lattice $N$ associated to $X$. For each cone $\sigma$ of
$\del$ there corresponds an orbit closure $V(\sigma)$ of the action of complex
torus on $X$. The homology classes $\{[V(\sigma)]\mid \dim \sigma=k\}$ form a
set of specified generators of $H_{n-k}(X,\Q)$.