(4, 0, 0, 0)
[polymake for n=5,6]
• Flow Polytopes of complete graph FLOW(n)= F(K_n) [arxiv] (Mészáros, Morales, Striker)
• Chan-Robbins-Yuen Polytopes CRY(n-1)
• convex_hull({incidence_vector_F | F a unit flow of the complete graph on n nodes})
• Volume equals product of the first n - 2 Catalan numbers
1, 3, 6, 10, 15,... (n-1 choose 2) [ OEIS A000217]
• Number of Vertices in nth polytope:
2, 4, 8, 16, 32 ... 2^(n-2) [ OEIS A000079]
• Number of Facets:
2, 4, 8, 13 ... OPEN [ OEIS ?]
• f-vectors:
1, 2, 1, 4, 6, 4, 1, 8, 26, 45, 45, 26, 8, 1, 16, 98, 327, 681, 944, 897, 588, 262, 76, 13... [ OEIS ?]