I am on a path to learn Blender, the open-source computer graphics software. This way, I can now start creating 3d visuals, rather than the plain old 2-dimensional imagery.
Since I have just started (and since I’m extremely busy with exams), I’ll do something really quick and small.
I’ll briefly describe what I’m talking about. A permutahedron of a symmetric group of order (denoted by ), which is nothing but the group of all permutations of distinct items, is an dimensional polyhedron in the space whose vertices are formed by the set .
In other words, take the coordinate and shuffle the numbers 1,2,3 etc. among themselves to get the vertices of the polyhedron.
Now when , this results in a hexagon inside . This fact is quite exciting to think about, so I made a little visualization of it. Here’s the output: