  We prove that every triconnected planar graph is definable by a first order
sentence that uses at most 15 variables and has quantifier depth at most
$11\log_2 n+43$. As a consequence, a canonic form of such graphs is computable
in $AC^1$ by the 14-dimensional Weisfeiler-Lehman algorithm. This provides
another way to show that the planar graph isomorphism is solvable in $AC^1$.
