Theorem. Let D be a finite distributive lattice with n join-irreducible elements. Then there exists a planar lattice L of  O(n²)

 elements with Con(L) D.

 G. Grätzer, H. Lakser and E. T. Schmidt,  Congruence lattices of small planar lattices, Proc. Amer. Math. Soc. 123 (1995),  2619-2623.

Example. Take the distributive lattice D given in Fugure 1 . The lattice L we obtain is shown in Figure 2