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Encyclopedia of Combinatorial Polytope Sequences

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Acyclotope (zigzag ladder graph)

(0, 12, 0, 0)

Quotientopes P , whose upper ideal of shards contains the basic shards, and (i, i+2, {i+1}), and (i, i+2, {}). [Pilaud, Santos]
Acyclotopes A(G) for zigzag ladder graph G, with n+1 nodes, and edges { i,i+1}, and {i,i+2}. [Zaslavsky]
Graphical zonotopes for zigzag ladder graph Z(G) [Postnikov]
Voronoi cells of cographical lattice for zigzag ladder graphs (primary parallelohedra, primary parallelotopes) [F. Vallentin]

0, 1, 2, 3, ... n
Number of Vertices in nth polytope:
1, 2, 6, 18, 54, 162, ... 2*3^n acyclic orientations of zigzag ladder [ OEIS A008776 ]
Number of Facets:
0, 2, 6, 12, 20, ... n^2+n directed edge cuts of the zigzag ladder on n+1 nodes [ OEIS A002378]
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The 3d case is the hexirhombic dodecahedron.