  We use a growth procedure for binary trees due to Luczak and Winkler, a
bijection between binary trees and irreducible quadrangulations of the hexagon
due to Fusy, Poulalhon and Schaeffer, and the classical angular mapping between
quadrangulations and maps, to define a growth procedure for maps. The growth
procedure is local, in that every map is obtained from its predecessor by an
operation that only modifies vertices lying on a common face with some fixed
vertex. As n tends to infinity, the probability that the n'th map in the
sequence is 3-connected tends to 2^8/3^6. The sequence of maps has an almost
sure limit G, and we show that G is the distributional local limit of large,
uniformly random 3-connected graphs.
