  Let a torus $T$ act smoothly on a compact smooth manifold $M$. If the
rational equivariant cohomology $H^*_T(M)$ is a free $H^*_T(pt)$-module, then
according to the Chang-Skjelbred Lemma, it can be determined by the
$1$-skeleton consisting of the $T$-fixed points and $1$-dimensional $T$-orbits
of $M$. When $M$ is an even-dimensional, orientable manifold with 2-dimensional
1-skeleton, Goresky, Kottwitz and MacPherson gave a graphic description of the
equivariant cohomology. In this paper, first we revisit the even-dimensional
GKM theory and introduce a notion of GKM covering, then we consider the case
when $M$ is an odd-dimensional, possibly non-orientable manifold with
$3$-dimensional $1$-skeleton, and give a graphic description of its equivariant
cohomology.
