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Encyclopedia of Combinatorial Polytope Sequences



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Acyclotope (fan graph)

(0, 8, 0, 4)

Acyclotopes A(F_1,n) for fan graphs F_1,n. [Zaslavsky]
Graphical zonotopes for fan graph Z(F_1,n) [Postnikov]
Voronoi cells of cographical lattice for fan 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 fan graph
[ OEIS A008776 ]
Number of Facets:
0, 2, 6, 12, 20, ... n^2+n directed edge cuts of the fan graph on n+1 nodes [ OEIS A002378]
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The 3d case is the hexirhombic dodecahedron.