Small Covers Over L(?)bells

In this paper, we calculate the number of equivariant diffeomorphism classes of small covers over Lobell. The notion of small cover is first introduced by Davis and Januszkiewicz [1], which gives a direct connection between equivariant topology and combinatorics. As shown in [1], all small covers over a simple convex polytope Pn correspond to all characteristic functions(Zn/2-colorings) defined on all facets of Pn. In abstract algebra, we are all familiar with the group action, such as orbit, Burnside Lem-ma. Based on this theory, we find the automorphism of Lobell, the coloring defined on Lobell, and for the further step, we get the number of equivariant diffeomorphism classes of small covers over Lobell, with Burnside Lemma applied.