(No 3d term.)
[polymake for n=3]
• Birkhoff polytopes B [wiki]
• assignment polytope
• Transportation polytope Trans_n(1, 1, . . . , 1) [arxiv] (Mészáros, Morales, Rhoades)
• perfect matching polytope of complete bipartite graph
• set of doubly stochastic matrices
• convex_hull({M | M an nxn permutation matrix})
0, 1, 4, 9, 16 ... (n-1)^2
• Number of Vertices in nth polytope:
1, 2, 6, 24, ... n! [ OEIS A000142]
• Number of Facets:
0, 2, 9, 16,... n^2 [ OEIS A000290]
• f-vectors:
1, 2, 1, 6, 15, 18, 9, 1 ... [ OEIS ?]