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Encyclopedia of Combinatorial Polytope Sequences



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Symmetric Path Polytope

(No 3d term)
[polymake for n=4,5]

s-t Path Polytopes of complete graph Path(n)= Path(K_n), n>1 [Springer] (A. Schrijver)
convex_hull({incidence_vector_F | F a path from node s to node t of the complete graph on n nodes})
Dimensions:
0, 1, 4, 8,... conject. (n choose 2)-2 [ OEIS A034856]
Number of Vertices in nth polytope:
1, 2, 5, 16, 65, ... Sum_{k=0..(n-2)} (n-2)!/k! [ OEIS A000522]
Number of Facets:
2, 5, 25, ... OPEN [ OEIS ?]
f-vectors:
1, 2, 1, 5, 10, 10, 5, 1, 16, 102, 334, 622, 685, 442, 156, 25, 1... [ OEIS ?]
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