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Encyclopedia of Combinatorial Polytope Sequences



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Acyclotope (Tadpole graph)

(0, 6, 0, 2)

Quotientopes P , whose upper ideal of shards contains the basic shards,
and (1, 3, {2}), and (1, 3, {}). [Pilaud, Santos]
Acyclotopes A(T_3,n) for tadpole graphs T_3,n, with n+3 nodes. [Zaslavsky]
Graphical zonotopes for tadpole graphs Z(T_3,n) [Postnikov]
Voronoi cells of cographical lattice for tadpole graphs T_3,n (primary parallelohedra, primary parallelotopes) [F. Vallentin]

Dimensions:
0, 1, 2, 3, ... n+2
Number of Vertices in nth polytope:
1, 2, 6, 12, 24, 48, ... 6*2^n acyclic orientations of the tadpole graph on n+3 nodes[ OEIS A007283]
Number of Facets:
0, 2, 6, 10, 14, ... 6+2n directed edge cuts of the tadpole graph on n+3 nodes [ OEIS A005843]
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The 3d case is the hexagonal prism.