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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] |
• Dimensions: 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.