Maximal intersecting families

We study maximum cardinality families of pairwise intersecting subsets of an n-set. We give some general results on the collection of all such families for a fixed set and introduce a useful operation of switching which allows us to transform any one such family to another. We use this operation to determine all possibilities for n = 6, and to answer two open questions on families which are regular (as hypergraphs). Although there are no regular maximal intersecting families for n = 2, 4, 8 there are for all larger powers of two. We also determine sharp bounds for the largest size of a regular maximal intersecting family with a member of size a.