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Encyclopedia of Combinatorial Polytope Sequences



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Acyclotope (cycle graph)

(0, 14, 0, 0)

Acyclotopes for cycle graph A(G) [ Zaslavsky]
Graphical zonotopes for cycle graph Z(G) [Postnikov]
Voronoi cells of cographical lattice for cycle graphs (primary parallelohedra, primary parallelotopes) [F. Vallentin]
Brillouin zone (Wigner-Seitz cell of reciprocal space) for Body Centered Cubic lattice in 3d [wiki]
Dimensions:
0, 1, 2, 3, ... n
Number of Vertices in nth polytope:
1, 2, 6, 14, 30, ... acyclic orientations of (n+1)-cycle = 2^(n+1) - 2 [ OEIS A000918]
Number of Facets:
0, 2, 6, 12, 20, ... directed edge cuts of the (n+1)-cycle = n^2+n [ OEIS A002378]
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The 3d case is the rhombic dodecahedron.