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Encyclopedia of Combinatorial Polytope Sequences


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Balanced Minimum Evolution Polytope

(No 3d term.)
[polymake for n=5,6]
[faces and facets](2 page pdf.)
  • BME polytopes P_n = BME(n) [arxiv] (D. Haws, T. Hodge, R. Yoshida)
    [almob] (Eickmeyer et. al.) [blog resources]
  • Balanced Minimal Evolution polytopes [arxiv], [arxiv](Forcey et. al.)
  • convex_hull({dist_vector_T | T a binary tree with n labeled leaves})
  • Dimensions (start n =3):
    0, 2, 5, 9, 14 ... (n choose 2)-n
  • Number of Vertices in nth polytope:
    1, 3, 15, 105, ... (2n-5)!! [ OEIS A001147][see: i]
  • Number of Facets:
    0, 3, 52, 90262... OPEN [ OEIS ?]
  • f-vectors:
    1, 3, 3, 1, 15, 105, 250, 210, 52, 1, 105, 5460... [ OEIS ?]
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