Obviously we have two triplets (3-lets),

where `` '' stands for the numbers included in a triplet.
However, the tiling which satisfies all the above symmetry
(thus the sum of the numbers in the triplet is the same number)
does not exist as well as in the case *N*=2.
We need to compromise on some triplets. If we give up
the symmetry along the one of two diagonal orientations,
we get a tiling pattern

by a set numbers (0,1,2) in base 3.