  R. Nandakumar asked whether there is a tiling of the plane by pairwise
incongruent triangles of equal area and equal perimeter. Recently a negative
answer was given by Kupavskii, Pach and Tardos. Still one may ask for weaker
versions of the problem, or for the analogue of this problem for quadrangles,
pentagons, or hexagons. Several answers were given by the first author in a
previous paper. Here we solve three further cases. In particular, our main
result shows that there are vertex-to-vertex tilings by pairwise incongruent
triangles of unit area and bounded perimeter.
