The permutahedron for n=5
These images were created by generating postscript through Maple.
They represent the left-weak order on permutations, that is, two permutations
are connected with a line if they are related by a transposition of
12, 23, 34, or 45. The rows a determined by the length of the permutation
and the horizontal position is determined by sorting the permutation in
reverse lex order. This minimizes the number of crossings in a natural
way but it may be possible to do better.
These images were created in Maple. I prefer the postscript file
because of the scaling problems that one has with the jpeg version, but
these may be useful. The pdf version is on one page and is useful
for printing, but the image is very small when scaled down to the 8 inch
width. I would like to embed this poset into a sphere so that it
is planar on the globe (as was done for n=4) but I am pretty sure that
this is not possible.
Click on the following links for larger image
Click on the following links for a larger image
Color: jpeg pdf
B&W: jpeg pdf