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Permutahedron for n=4
Permutahedron for n=5
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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.

associahedra tiling #1
associahedra tiling #1 with dual graph
assocahedra dual tiling #1
associahedra tiling #2
associadra tiling #2 with dual graph
associahedra dual tiling #2
associahedra tiling #3
associahedra tiling #3 with dual graph
associahedra dual tiling #3

Home
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Permutahedron for n=4
Permutahedron for n=5
Octahedron