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Encyclopedia of Combinatorial Polytope Sequences



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Splitohedron

(No 3d term.)
[polymake for n=5,6]
[MatLab code for running PolySplit]
[also need matrix generator]
[and branch and bound algorithm]
[and distance algorithm]
[and RF-metric algorithm]

Splitohedra Sp_n [arxiv] (S. Forcey, L. Keefe, W. Sands)
relaxation of the Balanced Minimum Evolution Polytope BME(n).
intersection of half-spaces{split-facets, intersecting cherry faces,
caterpillar facets and the cherry clade-faces
} from BME(n)
and also obeying the {Kraft equalities}.
Dimensions (start n =3):
0, 2, 5, 9, 14 ... (n choose 2)-n
Number of Vertices in nth polytope:
1, 3, 27, 2335, ... OPEN [ OEIS ?]
Number of Facets:
0, 3, 40, 85 ... OPEN [ OEIS ?]
f-vectors:
1, 3, 3, 1, 27, 165, 310, 210, 40, 1, 2335, ... [ OEIS ?]
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