Some tilings of the
plane with associahedra of type A_2
These pictures were produced with Geometer's Sketchpad. I was curious if it was possible
to tile the plane with copies of the associahedron of type A_2 and I found that it could be
done in an infinite number of ways (see the second tiling and flip any individual pair of
associahedra independently to create a new tiling). I don't know if any of these tilings
correspond to 'affine' associahedra. It seems as though only the third tiling is generated
solely by reflections and then it has 'gaps' which by coincidence (or not) look like
permutahedra. Grace a` Franco Saliola
for teaching me Geometer's Sketchpad enough to draw these.
These pictures are available in a single pdf file from which
I created the GIF pictures below.