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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.