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Encyclopedia of Combinatorial Polytope Sequences



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Associahedron

( 0, 3, 6, 0)

Associahedra K, Y [claymath] (J.L. Loday)
Stasheff polytopes
Type A associahedra [arxiv] (Fomin, Reading)
Secondary polytope of the set of vertices of a polygon [maa review] (Gelfand, Kapranov, Zelevinsky)
Newton polytope of the discriminant polynomial of the (integer coordinate) vertices of a polygon.
Fiber polytope of the simplex over a polygon. [jstor] (Billera, Sturmfels)
Path graph associahedra [arxiv] (Carr, Devadoss)
Path graph cubeahedra [arxiv] (Devadoss, Heath, Vipismakul)
Zig-zag poset associahedra [arxiv] (Devadoss et.al.)
(1,n) biassociahedra KK(n,1), KK(1,n) [arxiv] (Saneblidze, Umble)
alt. notation B^n_1, B^1_n [arxiv] (Markl)
Dimensions:
0, 1, 2, 3, ... n
Number of Vertices in nth polytope:
1, 2, 5, 14, 42, ... Catalan numbers [ OEIS A000108]
Number of Facets:
0, 2, 5, 9, 14, ... Triangular numbers minus one [ OEIS A000096 ]
f-vectors:
1, 2, 1, 5, 5, 1, 14, 21, 9, 1, 42, 84, 56, 14, 1, ... [ OEIS A033282]
h-vectors:
1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1... [ OEIS A001263]
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