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Encyclopedia of Combinatorial Polytope Sequences



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Permutohedron, permutahedron

(0, 6, 0, 8)

(Type A) Permutohedra/ permutahedra P, S [wiki]
Secondary polytopes of the prisms of simplices. [e-book] (Gelfand, Kapranov, Zelevinsky)
complete-graph-associahedra [arxiv] (S. Devadoss)
complete-graph-multiplihedra [arxiv] (Devadoss, Forcey)
Step 1 Bipermutohedra P^n_m [arxiv](M. Markl)[arxiv](S.Saneblidze, R. Umble)
Step 1 Biassociahedra K(n,m) = K^n_m [arxiv](M. Markl)[arxiv](S.Saneblidze, R. Umble)
Acyclotopes for complete graphs A(K_n) [ Zaslavsky]
Graphical zonotopes for complete graphs Z(K_n) [Postnikov]
Voronoi cells of cographical lattice for complete graphs (primary parallelohedra, primary parallelotopes) [F. Vallentin]
Brillouin zone (Wigner-Seitz cell of reciprocal space) for Face Centered Cubic lattice in 3d [wiki]
Poset-associahedra for antichain with minimal element adjoined [arxiv]
1-skeleton is Cayley graph for symmetric group, using transpositions.[wiki]
Dimensions:
0, 1, 2, 3, ... n
Number of Vertices in nth polytope:
1, 2, 6, 24, 120, ... n! [ OEIS A000142]
Number of Facets:
0, 2, 6, 14, 30 ... 2^(n+1) -2 [ OEIS A000918]
f-vectors:
1, 2, 1, 6, 6, 1, 24, 36, 14, 1, ... [ OEIS A019538]
h-vectors:
1, 4, 1, 1, 11, 11, 1, 1, 26, 66, 26, 1, ... [ OEIS A008292]
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