polyomino graphs

[Jonathan Post]

This is very close to the the Delaunay triangulation dual to the
Voronoi diagram (Dirichlet tessellation) of a polyomino. It is not, of
course, a triangulation, because the centroids of 4 monominoes meeting
at a common vertex is itself a square (tilted 45 degrees).

A Voronoi tessellation is called centroidal when the generating point
of each cell is also its mean (center of mass).