Atoms and coatoms in three-generated lattices

In addition to the unique cover $M^+$ of variety modular lattices, we also deal with those twenty-three known covers that can be extracted from literature. For and for each these varieties covering it, determine what pair formed by number atoms coatoms a three-generated lattice belonging in question be. Furthermore, $W$ lattices is obtained forming join some mentioned above, is, $2^{23}$ possible choices $W$, how many have. The greatest occurring this way only six. order point out need not so larger varieties, construct $47\,092$-element has exactly eighteen atoms. purely theoretical proofs, which constitute majority paper, computer-assisted arguments are presented.