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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] • Zonotopes polar to the braid arrangements. • Quotientopes P , whose upper ideal of shards contains all the shards. [Pilaud, Santos] • Fiber polytopes of unit cubes over line segments. • 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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