page_title: Permutohedron
hierarchical_section_title: Permutohedron
caption_attribution_description: the six edge directions Permutohedron of the symmetric group S4 Parallel edges have the same color. The color shows which two places are swapped, as indicated by the triangle of pairs in the bottom right corner. In the bottom vertex of an edge the elements on these two places are in their natural order, and in the top vertex they are reversed. (Consequently, the bottom vertex of the whole diagram is completely in natural order, and the top vertex is completely reversed.) This &#32;image&#32;was created with POV-Ray. trunc_octa_perm.pov
context_page_description: In mathematics, the permutohedron of order n is an-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates are the permutations of the first n natural numbers. The edges are the shortest possible connections between these points. Two permutations connected by an edge differ in two places, and the numbers on these places are neighbors.
  The image on the right shows the permutohedron of order 4, which is the truncated octahedron. Its vertices are the 24 permutations of. Parallel edges have the same edge color. The 6 edge colors correspond to the 6 possible transpositions of 4 elements, i.e. they indicate in which two places the connected permutations differ.
context_section_description: In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates are the permutations of the first n natural numbers. The edges are the shortest possible connections between these points. Two permutations connected by an edge differ in two places, and the numbers on these places are neighbors.
  The image on the right shows the permutohedron of order 4, which is the truncated octahedron. Its vertices are the 24 permutations of (1, 2, 3, 4). Parallel edges have the same edge color. The 6 edge colors correspond to the 6 possible transpositions of 4 elements, i.e. they indicate in which two places the connected permutations differ. (E.g. red edges connect permutations that differ in the last two places.)
caption: The permutohedron of order 4
exif: {}