The final publication is available at Springer via DOI 10.1007/s00454-015-9735-5

The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-Level matroids generalize series-parallel graphs, which have been already successfully analyzed from the enumerative perspective. We bring to light some structural properties of 2-level matroids and exploit them for enumerative purposes. Moreover, the counting results are used to show that the number of combinatorially non-equivalent (n-1)(n-1)-dimensional 2-level polytopes is bounded from below by c·n-5/2·¿-nc·n-5/2·¿-n, where c˜0.03791727c˜0.03791727 and ¿-1˜4.88052854¿-1˜4.88052854.