Encyclopedia of Combinatorial Polytope Sequences

 Instructions. Five dimensional BME. n=6 Caterpillar facet. n=6 Intersecting-cherry facet.

Back to big table.

[text version]

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CAVEATS
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1) Note that if you are using the browser-based polymake like me (http://shell.polymake.org/) or (http://polymake.org/doku.php/boxdoc) you can copy from my stuff and paste into the browser by right-clicking. Be careful though because your browser/clipboard may insert line breaks, which mess it up for a big entry. Paste into notepad first and remove them.
2) I left the prompt “polytope >” in. Remove this.
3) Underscores like in F_VECTOR get removed sometimes and need replaced. Can be done in the pasting box in polymake.
4) The output below for VERTICES_IN_FACETS gives lists of the vertices, numbered 0-14, based on the order they were entered.
The pictures with the numbering 0-14 are here.
To see one of the 4d facets, you can go back and get those vertices from the original input, and make a new polytope with just those! For an example, see the facet from {0 2 3 4 7 14} here.
5) The points here are integers via multiplying the usual ones by 8. I put the initial “1” in each point.

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INPUT/OUTPUT
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polytope > \$points=new Matrix([[1,4,1,1,2,1,1,2,4,2,2],[1,4,2,1,1,2,1,1,2,2,4],[1,4,1,2,1,1,2,1,2,4,2],[1,2,1,4,1,2,2,2,1,4,1],[1,2,2,2,2,1,4,1,1,4,1],[1,1,4,1,2,1,4,2,1,2,2],[1,1,2,1,4,2,4,1,2,2,1],[1,2,1,1,4,2,2,2,4,1,1],[1,1,1,2,4,4,2,1,2,1,2],[1,1,1,4,2,4,1,2,1,2,2],[1,2,2,2,2,4,1,1,1,1,4],[1,2,4,1,1,2,2,2,1,1,4],[1,1,4,2,1,1,2,4,2,1,2],[1,1,2,4,1,2,1,4,2,2,1],[1,2,2,2,2,1,1,4,4,1,1]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

15 105 250 210 52

polytope > print \$p->VERTICES_IN_FACETS;

{0 2 4 5 12 14}
{0 2 3 7 8 9}
{0 2 3 4 7 14}
{2 3 4 8 9 10}
{2 3 4 6 7 8}
{2 3 4 12 13 14}
{2 3 4 5 11 12}
{0 2 3 13 14}
{0 2 4 6 7}
{3 4 5 9 10 11}
{7 8 10 11 12 14}
{5 8 9 10 11 12}
{5 6 7 8 11 12}
{3 5 9 11 12 13}
{5 6 8 10 11}
{9 10 11 12 13}
{3 4 6 7 13 14}
{4 5 6 12 13 14}
{3 4 5 6 9 13}
{3 4 5 12 13}
{3 4 6 8 9}
{3 6 7 8 9 13}
{5 6 8 9 12 13}
{7 8 9 13 14}
{5 6 7 12 14}
{6 7 8 12 13 14}
{8 9 10 12 13 14}
{4 5 6 8 9 10}
{0 7 8 9 10 14}
{0 3 7 9 13 14}
{0 4 5 6 7 14}
{0 5 7 11 12 14}
{0 1 7 8 10}
{0 1 11 12 14}
{1 2 4 5 11}
{1 2 3 9 10}
{0 1 7 10 11 14}
{0 1 5 6 7 11}
{0 1 9 10 13 14}
{1 3 9 10 11 13}
{1 10 11 12 13 14}
{1 6 7 8 10 11}
{1 4 5 6 10 11}
{1 2 3 4 10 11}
{1 2 3 11 12 13}
{1 2 4 6 8 10}
{0 1 2 6 7 8}
{0 1 2 8 9 10}
{0 1 2 3 9 13}
{0 1 2 12 13 14}
{0 1 2 5 11 12}
{0 1 2 4 5 6}

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Facet: {0 2 3 4 7 14}
---------------------

\$points=new Matrix([[1,4,1,1,2,1,1,2,4,2,2],[1,4,1,2,1,1,2,1,2,4,2],[1,2,1,4,1,2,2,2,1,4,1],[1,2,2,2,2,1,4,1,1,4,1],[1,2,1,1,4,2,2,2,4,1,1],[1,2,2,2,2,1,1,4,4,1,1]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

6 15 18 9

polytope > print \$p->VERTICES_IN_FACETS;

{0 2 4 5}
{0 3 4 5}
{2 3 4 5}
{1 2 3 5}
{0 1 3 5}
{0 1 2 5}
{1 2 3 4}
{0 1 3 4}
{0 1 2 4}

A 6-leaved caterpillar facet: 8 dimensional facet of 9 dim BME(6)

polytope > \$points=new Matrix([[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,8,4 ,1,2,1,2,8,4,4,1,2,2,4,4],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,8,2,1,4,1,4,8,2,2,1 ,4,4,4,2],[1,1,8,1,2,4,1,8,4,2,1,2,4,4,2,4],[1,1,8,1,4,2,1,8,2,4,1,4,2,2,4,4],[1,1,4 ,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,1,4,8,1,2,2,1,8,4,4,2,4,1,2,4],[1,1,4,2,8,1,2,4,1,8,4 ,4,2,2,4,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,4,1,8,2,2,8,1,4,2,4,4,1,4,2],[1,1 ,4,1,2,8,2,8,4,1,2,4,4,4,1,2],[1,1,2,8,4,1,4,1,2,8,2,4,4,4,1,2],[1,1,2,8,1,4,4,1,8,2 ,2,4,4,1,4,2],[1,1,2,4,8,1,4,2,1,8,4,2,4,4,2,1],[1,1,2,4,1,8,4,2,8,1,4,4,2,2,4,1],[1 ,1,2,1,8,4,4,8,1,2,4,2,4,1,2,4],[1,1,2,1,4,8,4,8,2,1,4,4,2,2,1,4],[1,1,1,8,4,2,8,1,2 ,4,1,2,4,4,2,4],[1,1,1,8,2,4,8,1,4,2,1,4,2,2,4,4],[1,1,1,4,8,2,8,2,1,4,2,1,4,4,4,2], [1,1,1,4,2,8,8,2,4,1,2,4,1,4,4,2],[1,1,1,2,8,4,8,4,1,2,4,1,2,2,4,4],[1,1,1,2,4,8,8,4 ,2,1,4,2,1,4,2,4]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

24 276 1872 6216 10336 8352 2952 340

polytope > print \$p->VERTICES_IN_FACETS;

{1 2 3 5 8 10 13 15 19 20 21 22}
{1 2 3 5 6 7 9 11 13 15}
{1 2 3 5 7 10 12 13 18 20}
{1 2 3 5 8 9 15 17 22 23}
{1 2 3 5 7 8 9 10 13 15}
{1 2 3 7 8 10 12 13 14 20}
{1 2 5 7 8 10 13 18 19 20}
{1 2 6 7 8 12 13 18 19 20}
{1 4 5 6 7 11 13 15 17 19}
{1 5 6 7 8 10 13 15 16 17 19 22}
{1 5 6 7 8 9 10 11 15 17}
{1 5 6 7 8 10 18 19 20 22}
{1 6 7 8 13 14 15 19 20 22}
{1 4 7 9 11 15 17 19 21 23}
{1 3 4 7 9 13 15 17 19 23}
{1 3 4 7 13 16 17 19 22 23}
{1 3 7 8 9 10 13 14 15 16 20 22}
{1 3 7 9 13 15 18 19 20 21 22 23}
{1 3 7 9 13 15 16 17 22 23}
{1 3 7 9 12 13 14 15 18 20}
{1 3 5 8 9 10 15 16 17 22}
{1 3 4 5 13 15 16 17 19 22}
{1 3 4 5 15 17 19 21 22 23}
{1 3 4 5 7 10 12 14 18 20}
{1 3 4 5 7 9 10 11 13 15 16 17}
{1 3 4 5 7 10 13 16 18 19 20 22}
{1 2 3 5 8 16 17 22}
{1 2 3 5 13 18 19 20}
{1 2 3 5 10 12 14 20}
{1 2 3 5 15 21 22 23}
{1 2 3 8 13 14 15 20}
{1 2 5 6 7 8 13 15}
{1 2 5 6 7 8 13 19}
{1 2 5 6 8 13 15 19}
{1 2 5 6 7 8 9 15}
{1 2 5 6 7 8 18 19}
{1 6 7 15 19 21 22 23}
{1 6 7 8 12 13 14 20}
{1 6 7 15 19 20 21 22}
{1 3 4 7 18 19 22 23}
{1 3 5 10 13 15 16 22}
{1 3 4 5 6 7 11 13}
{1 3 4 7 10 14 16 20}
{1 3 4 5 8 9 10 16}
{1 3 4 7 9 16 17 23}
{1 3 4 9 15 19 21 23}
{1 3 13 15 17 19 22 23}
{1 3 12 13 15 18 20 21}
{1 7 9 14 15 20 22 23}
{1 7 13 15 17 19 22 23}
{1 4 5 7 13 16 17 19}
{1 6 7 15 17 19 22 23}
{1 7 8 10 13 19 20 22}
{1 7 8 9 10 15 16 17}
{1 6 7 11 15 17 19 21}
{1 6 7 15 17 19 21 23}
{3 4 5 10 13 15 16 19 21 22}
{3 4 5 10 11 15 16 17 21 22}
{3 5 9 10 11 15 17 21 22 23}
{3 9 10 11 13 15 16 20 21 22}
{3 4 9 11 18 19 20 21 22 23}
{3 4 9 11 13 16 18 19 20 22}
{3 4 8 9 10 11 14 16 20 22}
{3 4 6 7 9 11 12 13 18 19}
{3 4 6 7 8 9 10 11 12 14}
{3 4 7 9 10 11 12 13 14 16 18 20}
{3 4 7 9 13 16 18 19 22 23}
{3 4 9 11 13 15 16 17 19 21 22 23}
{3 4 10 11 13 16 19 20 21 22}
{3 4 5 7 10 12 13 18}
{3 4 5 10 19 20 21 22}
{3 4 5 10 11 13 15 21}
{3 4 5 11 17 21 22 23}
{3 8 9 10 15 20 21 22}
{3 4 7 9 13 16 17 23}
{3 4 10 11 13 15 16 21}
{3 9 11 13 19 20 21 22}
{3 9 11 12 13 18 20 21}
{3 9 11 12 13 18 19 21}
{3 9 11 13 18 19 20 21}
{3 9 10 11 15 16 17 22}
{3 7 8 9 10 12 13 14}
{3 7 9 13 16 18 20 22}
{3 6 9 11 12 13 19 21}
{3 9 12 13 15 18 20 21}
{4 7 9 11 13 16 17 18 19 23}
{4 6 7 11 17 18 19 23}
{4 6 7 10 11 12 14 16}
{4 8 9 11 14 16 22 23}
{4 7 9 11 13 15 17 19}
{4 9 11 16 18 19 22 23}
{4 9 11 14 16 20 22 23}
{4 9 11 16 18 20 22 23}
{4 9 11 14 16 18 20 23}
{4 11 14 16 17 18 20 23}
{4 10 11 13 16 18 19 20}
{7 9 13 14 15 16 18 20 22 23}
{7 9 12 13 14 15 16 17 18 23}
{7 9 11 12 13 16 17 18}
{7 12 13 14 16 18 22 23}
{7 13 14 15 18 19 20 22}
{9 11 13 15 16 17 18 20 21 23}
{9 11 13 16 18 19 20 21 22 23}
{9 11 12 14 15 17 18 20 21 23}
{9 11 12 13 14 15 16 17 18 20}
{9 10 11 13 14 15 16 20}
{9 11 14 16 17 18 20 23}
{9 11 12 13 15 18 20 21}
{9 13 15 16 20 21 22 23}
{9 14 15 16 17 18 20 23}
{12 13 14 15 16 17 18 19 20 21 22 23}
{11 12 13 15 17 18 20 21}
{11 13 16 17 18 19 21 23}
{10 12 16 17 18 19 20 22}
{10 12 13 14 16 19 20 21}
{10 11 12 13 16 17 18 19 20 21}
{10 11 12 13 14 15 16 17 20 21}
{8 12 14 17 20 21 22 23}
{8 14 15 16 17 19 21 22}
{8 10 15 16 17 19 21 22}
{8 10 11 12 14 15 17 21}
{8 10 12 13 14 19 20 21}
{8 10 12 13 14 15 16 17 19 21}
{8 10 12 14 16 17 19 20 21 22}
{8 10 12 17 18 19 20 21 22 23}
{8 10 13 14 15 16 19 20 21 22}
{8 9 10 11 14 15 16 17 20 21 22 23}
{6 8 10 12 13 16 17 19}
{6 12 13 15 17 19 22 23}
{6 12 14 15 18 19 21 23}
{6 7 13 15 17 19 22 23}
{6 7 12 14 16 18 22 23}
{6 7 8 13 14 15 16 22}
{6 7 9 12 14 15 17 23}
{6 8 12 14 15 17 19 21 22 23}
{6 8 12 13 14 15 16 17 19 22}
{6 7 12 13 14 15 16 17 22 23}
{6 7 12 13 14 15 18 19 22 23}
{6 7 12 13 16 17 18 19 22 23}
{6 7 14 15 18 19 20 21 22 23}
{6 7 9 11 12 13 15 17 18 19 21 23}
{6 7 8 10 12 13 14 16 18 19 20 22}
{6 7 8 9 10 11 12 13 14 15 16 17}
{5 6 7 10 16 18 19 22}
{5 6 8 10 12 14 16 18}
{5 6 7 10 11 13 15 17}
{5 8 10 17 18 19 22 23}
{5 8 9 10 15 17 22 23}
{5 8 10 15 17 21 22 23}
{5 8 10 17 19 21 22 23}
{5 8 10 15 17 19 21 22}
{5 10 15 16 17 19 21 22}
{5 10 11 12 17 18 19 21}
{4 5 14 16 17 18 20 23}
{4 5 15 16 17 19 21 22}
{5 6 8 10 12 16 17 18 19 22}
{4 5 10 11 13 15 16 17 19 21}
{4 5 10 11 12 14 16 17 18 20}
{4 5 10 11 16 17 18 19 20 21 22 23}
{4 5 6 7 10 11 12 13 16 17 18 19}
{2 8 12 13 14 19 20 21}
{2 8 10 11 14 16 17 23}
{2 8 10 12 18 20 21 23}
{2 8 10 12 13 19 20 21}
{2 8 10 12 13 18 19 20}
{2 8 10 12 18 19 20 21}
{2 7 8 10 12 13 18 20}
{2 6 8 12 17 19 21 23}
{2 5 6 8 12 16 17 22}
{2 5 10 11 12 14 17 20}
{2 4 5 11 18 20 21 23}
{2 4 5 10 11 12 14 20}
{2 4 5 10 16 20 22 23}
{2 4 5 6 11 12 13 19}
{2 6 8 9 11 12 13 15}
{2 8 9 11 14 20 21 23}
{2 3 4 8 10 11 20 22}
{2 3 5 9 10 11 13 15}
{2 3 5 9 10 11 15 21}
{2 3 5 10 11 13 15 21}
{2 3 4 5 11 13 15 21}
{2 3 5 9 10 11 21 23}
{2 3 5 7 9 10 11 13}
{2 3 4 6 8 10 11 12}
{2 3 4 10 11 12 14 20}
{2 3 4 8 10 11 12 14}
{2 3 4 8 10 11 14 20}
{2 3 4 5 10 12 14 20}
{2 4 5 10 11 14 16 17 20 23}
{2 4 5 11 12 14 17 18 20 23}
{2 5 10 11 12 17 18 20 21 23}
{2 5 8 10 12 14 16 17 18 20 22 23}
{2 5 6 8 12 17 18 19 22 23}
{2 5 6 8 10 11 12 13 15 17 19 21}
{2 5 8 10 12 17 18 19 21 23}
{2 5 8 10 18 19 20 21 22 23}
{2 5 8 9 10 11 15 17 21 23}
{2 5 6 7 8 10 12 13 18 19}
{2 5 6 7 8 9 10 11 13 15}
{2 8 10 11 12 14 17 20 21 23}
{2 4 8 10 11 14 16 20 22 23}
{2 3 6 7 8 9 10 11 12 13}
{2 3 8 9 10 11 20 21 22 23}
{2 3 4 5 10 11 20 21 22 23}
{2 3 4 5 6 7 10 11 12 13}
{2 3 4 8 9 11 14 20 22 23}
{2 3 8 9 10 11 12 13 14 15 20 21}
{2 3 5 8 9 10 15 21 22 23}
{2 3 4 5 10 11 12 13 18 19 20 21}
{2 3 4 5 8 9 10 11 16 17 22 23}
{0 6 9 11 12 18 21 23}
{0 6 8 9 11 14 16 17}
{0 6 7 10 14 16 18 20}
{0 4 5 6 12 16 17 18}
{0 6 7 9 12 13 15 21}
{0 3 4 6 7 9 18 19}
{0 3 4 7 9 12 14 18}
{0 3 4 6 7 9 12 14}
{0 3 4 6 7 9 12 18}
{0 6 12 14 16 18 22 23}
{0 2 4 11 12 14 17 23}
{0 2 12 14 16 18 22 23}
{0 2 5 8 14 18 20 22}
{0 2 4 5 6 7 10 12}
{0 2 3 4 11 13 15 21}
{0 2 3 4 12 18 19 21}
{0 2 5 6 18 19 22 23}
{0 2 3 4 14 20 22 23}
{0 2 3 4 9 16 17 23}
{0 2 3 9 12 14 15 21}
{0 2 5 6 8 16 17 22}
{0 2 5 6 11 15 17 21}
{0 2 4 5 8 9 11 17}
{0 2 12 13 14 19 20 21}
{0 6 8 14 15 21 22 23}
{0 3 4 6 7 8 9 14}
{0 6 7 14 18 20 21 23}
{0 6 7 14 18 20 22 23}
{0 6 7 14 16 18 20 22}
{0 6 7 14 16 18 22 23}
{0 1 4 7 9 11 21 23}
{0 1 4 7 9 11 17 23}
{0 1 4 7 9 10 11 16}
{0 1 4 7 9 11 16 17}
{0 1 5 6 8 10 20 22}
{0 1 5 6 8 10 16 22}
{0 1 4 5 16 18 20 22}
{0 1 4 5 17 19 21 23}
{0 1 5 6 8 10 11 17}
{0 1 5 6 8 10 16 17}
{0 1 4 7 9 16 17 23}
{0 1 7 9 12 14 15 18}
{0 1 3 9 18 20 21 23}
{0 1 3 7 13 18 19 21}
{0 1 4 5 7 12 14 18}
{0 1 2 6 8 13 15 19}
{0 1 6 8 13 14 15 19}
{0 1 2 5 8 16 17 22}
{0 1 5 6 8 16 17 22}
{0 1 2 8 9 15 17 23}
{0 1 2 8 19 20 21 22}
{0 1 3 4 9 16 17 23}
{0 1 2 3 6 9 11 15}
{0 1 2 5 6 13 15 19}
{0 1 4 5 6 13 15 19}
{0 1 2 3 7 8 10 14}
{0 1 2 6 12 18 19 20}
{0 1 3 8 9 14 16 22}
{0 1 3 4 7 12 14 18}
{0 1 3 7 9 12 14 18}
{0 2 3 4 9 11 12 14 18 20 21 23}
{0 2 3 4 6 11 12 13 19 21}
{0 2 3 4 8 9 14 16 22 23}
{0 2 3 6 9 11 12 13 15 21}
{0 2 4 8 9 11 14 16 17 23}
{0 2 6 8 12 14 16 17 22 23}
{0 2 6 8 12 13 14 15 19 21}
{0 2 6 8 9 11 12 14 15 17 21 23}
{0 2 6 8 12 14 18 19 20 21 22 23}
{0 2 5 6 12 16 17 18 22 23}
{0 2 5 6 8 12 14 16 18 22}
{0 2 4 5 12 14 16 17 18 23}
{0 2 4 5 14 16 18 20 22 23}
{0 2 4 5 6 11 13 15 19 21}
{0 2 4 5 6 11 12 17 18 19 21 23}
{0 2 4 5 6 8 10 11 12 14 16 17}
{0 2 3 4 6 7 8 10 12 14}
{0 2 3 4 6 8 9 11 12 14}
{0 4 5 6 7 10 12 14 16 18}
{0 5 6 8 10 14 16 18 20 22}
{0 6 7 9 12 14 15 18 21 23}
{0 4 6 7 8 9 10 11 14 16}
{0 4 6 7 9 11 18 19 21 23}
{0 4 6 7 9 11 12 14 16 17 18 23}
{0 3 6 7 9 12 13 18 19 21}
{0 3 4 6 9 11 12 18 19 21}
{0 1 6 7 8 9 10 11 16 17}
{0 1 6 7 9 11 15 17 21 23}
{0 1 6 7 8 10 14 16 20 22}
{0 1 4 5 8 9 10 11 16 17}
{0 1 4 5 6 7 10 11 16 17}
{0 1 6 7 18 19 20 21 22 23}
{0 1 6 7 14 15 20 21 22 23}
{0 1 2 3 12 13 14 15 20 21}
{0 1 2 3 8 9 16 17 22 23}
{0 1 2 3 12 13 18 19 20 21}
{0 1 2 3 4 5 8 9 16 17}
{0 1 2 3 4 5 16 17 22 23}
{0 1 3 4 7 9 14 16 18 20 22 23}
{0 1 3 4 6 7 9 11 13 15 19 21}
{0 1 3 4 7 9 18 19 21 23}
{0 1 3 4 7 8 9 10 14 16}
{0 1 3 7 9 12 13 15 18 21}
{0 1 3 9 12 14 15 18 20 21}
{0 1 4 6 7 11 17 19 21 23}
{0 1 7 9 14 15 18 20 21 23}
{0 1 6 8 14 15 19 20 21 22}
{0 1 6 7 12 13 14 15 18 19 20 21}
{0 1 6 7 8 9 14 15 16 17 22 23}
{0 1 5 6 7 10 16 18 20 22}
{0 1 4 5 6 11 15 17 19 21}
{0 1 4 5 7 10 14 16 18 20}
{0 1 4 5 6 7 16 17 18 19 22 23}
{0 1 2 8 13 14 15 19 20 21}
{0 1 2 6 8 12 13 14 19 20}
{0 1 2 5 6 8 18 19 20 22}
{0 1 2 5 6 8 9 11 15 17}
{0 1 2 3 4 5 6 11 13 15}
{0 1 2 3 4 5 13 15 19 21}
{0 1 2 3 4 5 12 14 18 20}
{0 1 2 3 4 5 7 10 12 14}
{0 1 2 5 6 8 15 17 19 21 22 23}
{0 1 2 5 6 7 8 10 12 14 18 20}
{0 1 2 3 8 9 14 15 20 21 22 23}
{0 1 2 3 6 7 8 9 12 13 14 15}
{0 1 2 3 4 5 9 11 15 17 21 23}
{0 1 2 3 4 5 8 10 14 16 20 22}
{0 1 2 3 4 5 6 7 12 13 18 19}
{0 1 2 3 4 5 6 7 8 9 10 11}
{0 1 2 3 4 5 18 19 20 21 22 23}

Try the subfacet: {0 1 2 3 4 5 6 7 8 9 10 11}

polytope > \$points=new Matrix([[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,8,4,1,2,1,2,8,4,4,1,2,2,4,4],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,8,2,1,4,1,4,8,2,2,1,4,4,4,2],[1,1,8,1,2,4,1,8,4,2,1,2,4,4,2,4],[1,1,8,1,4,2,1,8,2,4,1,4,2,2,4,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,1,4,8,1,2,2,1,8,4,4,2,4,1,2,4],[1,1,4,2,8,1,2,4,1,8,4,4,2,2,4,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,4,1,8,2,2,8,1,4,2,4,4,1,4,2],[1,1,4,1,2,8,2,8,4,1,2,4,4,4,1,2]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->VERTICES_IN_FACETS;

polytope > print \$p->F_VECTOR;

12 66 216 417 446 228 39

polytope > print \$p->VERTICES_IN_FACETS;

{1 2 3 5 6 7 9 11}
{1 2 3 5 7 8 9 10}
{1 3 4 5 7 9 10 11}
{1 2 5 6 7 8 9}
{1 5 6 7 8 9 10 11}
{1 3 4 5 6 7 11}
{1 3 4 5 8 9 10}
{3 4 6 7 8 9 10 11}
{2 3 5 7 9 10 11}
{2 3 4 6 8 10 11}
{2 5 6 7 8 9 10 11}
{2 3 6 7 8 9 10 11}
{2 3 4 5 8 9 10 11}
{2 3 4 5 6 7 10 11}
{0 2 4 5 8 9 11}
{0 2 4 5 6 7 10}
{0 4 6 7 8 9 10 11}
{0 3 4 6 7 8 9}
{0 1 6 7 8 9 10 11}
{0 1 4 7 9 10 11}
{0 1 5 6 8 10 11}
{0 1 2 3 7 8 10}
{0 1 2 3 6 9 11}
{0 2 3 4 6 8 9 11}
{0 2 4 5 6 8 10 11}
{0 2 3 4 6 7 8 10}
{0 1 3 4 7 8 9 10}
{0 1 4 5 8 9 10 11}
{0 1 3 4 6 7 9 11}
{0 1 4 5 6 7 10 11}
{0 1 2 3 4 5 8 10}
{0 1 2 3 4 5 7 10}
{0 1 2 5 6 7 8 10}
{0 1 2 3 4 5 9 11}
{0 1 2 3 4 5 6 11}
{0 1 2 5 6 8 9 11}
{0 1 2 3 6 7 8 9}
{0 1 2 3 4 5 8 9}
{0 1 2 3 4 5 6 7}

Try the subfacet: {0 1 2 3 4 5 6 7}

polytope > \$points=new Matrix([[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,8,4,1,2,1,2,8,4,4,1,2,2,4,4],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,8,2,1,4,1,4,8,2,2,1,4,4,4,2],[1,1,8,1,2,4,1,8,4,2,1,2,4,4,2,4],[1,1,8,1,4,2,1,8,2,4,1,4,2,2,4,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,1,4,8,1,2,2,1,8,4,4,2,4,1,2,4]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

8 28 54 60 37 11

polytope > print \$p->VERTICES_IN_FACETS;

{1 3 4 5 6 7}
{2 3 4 5 6 7}
{1 2 3 5 6 7}
{0 1 2 5 6 7}
{0 1 2 3 6 7}
{0 2 4 5 6 7}
{0 1 4 5 6 7}
{0 2 3 4 6 7}
{0 1 3 4 6 7}
{0 1 2 3 4 5 6}
{0 1 2 3 4 5 7}

Try the subfacet: {0 1 2 3 4 5 6}

polytope > \$points=new Matrix([[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,8,4,1,2,1,2,8,4,4,1,2,2,4,4],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,8,2,1,4,1,4,8,2,2,1,4,4,4,2],[1,1,8,1,2,4,1,8,4,2,1,2,4,4,2,4],[1,1,8,1,4,2,1,8,2,4,1,4,2,2,4,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

7 21 33 27 10

polytope > print \$p->VERTICES_IN_FACETS;

{1 3 4 5 6}
{2 3 4 5 6}
{1 2 3 5 6}
{0 1 2 5 6}
{0 1 2 3 6}
{0 2 4 5 6}
{0 1 4 5 6}
{0 2 3 4 6}
{0 1 3 4 6}
{0 1 2 3 4 5}

Try the subfacet: {0 1 2 3 4 5}

polytope > \$points=new Matrix([[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,8,4,1,2,1,2,8,4,4,1,2,2,4,4],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,8,2,1,4,1,4,8,2,2,1,4,4,4,2],[1,1,8,1,2,4,1,8,4,2,1,2,4,4,2,4],[1,1,8,1,4,2,1,8,2,4,1,4,2,2,4,4]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

6 15 18 9

polytope > print \$p->VERTICES_IN_FACETS;

{1 3 4 5}
{2 3 4 5}
{1 2 3 5}
{0 1 2 5}
{0 1 2 3}
{0 2 4 5}
{0 1 4 5}
{0 2 3 4}
{0 1 3 4}

------------------
Here are the points for a pair of intersecting cherries {1,6} and {2,6} for n=6, calculated in two sets for the two cherries:
------------------

\$points=new Matrix([[1,4,1,1,2,8,2,2,4,4,8,4,1,4,1,2],[1,4,2,1,1,8,4,2,2,4,4,4,2,8,1,1],[1,4,1,2,1,8,2,4,2,4,4,8,1,4,2,1],[1,2,1,4,1,8,4,4,4,2,2,8,1,2,4,1],[1,2,2,2,2,8,2,8,2,2,2,8,2,2,2,2],[1,1,4,1,2,8,2,8,4,1,2,4,4,4,1,2],[1,1,2,1,4,8,4,8,2,1,4,4,2,2,1,4],[1,2,1,1,4,8,4,4,4,2,8,2,1,2,1,4],[1,1,1,2,4,8,8,4,2,1,4,2,1,4,2,4],[1,1,1,4,2,8,8,2,4,1,2,4,1,4,4,2],[1,2,2,2,2,8,8,2,2,2,2,2,2,8,2,2],[1,2,4,1,1,8,4,4,4,2,2,2,4,8,1,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,2,4,1,8,4,2,8,1,4,4,2,2,4,1],[1,2,2,2,2,8,2,2,8,2,8,2,2,2,2,2],[1,4,2,2,4,4,1,1,2,8,8,4,1,4,1,2],[1,4,4,2,2,4,2,1,1,8,4,4,2,8,1,1],[1,4,2,4,2,4,1,2,1,8,4,8,1,4,2,1],[1,2,2,8,2,2,2,2,2,8,2,8,2,2,2,2],[1,2,4,4,4,2,1,4,1,8,2,8,1,2,4,1],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,1,4,2,8,1,2,4,1,8,4,4,2,2,4,1],[1,2,2,2,8,2,2,2,2,8,8,2,2,2,2,2],[1,1,2,4,8,1,4,2,1,8,4,2,4,4,2,1],[1,1,2,8,4,1,4,1,2,8,2,4,4,4,1,2],[1,2,4,4,4,2,4,1,1,8,2,2,4,8,1,1],[1,2,8,2,2,2,2,2,2,8,2,2,2,8,2,2],[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,2,4,4,4,2,1,1,4,8,8,2,1,2,1,4]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

30 435 3194 11127 19586 17694 7728 1282

-----------------
Here they are again in different order, as calculated by Bill Sands:
-----------------
\$points=new Matrix([[1,4,1,1,2,8,2,2,4,4,8,4,1,4,1,2],[1,4,1,2,1,8,2,4,2,4,4,8,1,4,2,1],[1,4,2,1,1,8,4,2,2,4,4,4,2,8,1,1],[1,2,1,1,4,8,4,4,4,2,8,2,1,2,1,4],[1,1,2,1,4,8,4,8,2,1,4,4,2,2,1,4],[1,1,1,2,4,8,8,4,2,1,4,2,1,4,2,4],[1,2,1,4,1,8,4,4,4,2,2,8,1,2,4,1],[1,1,2,4,1,8,4,2,8,1,4,4,2,2,4,1],[1,1,1,4,2,8,8,2,4,1,2,4,1,4,4,2],[1,2,4,1,1,8,4,4,4,2,2,2,4,8,1,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,4,1,2,8,2,8,4,1,2,4,4,4,1,2],[1,2,2,2,2,8,2,2,8,2,8,2,2,2,2,2],[1,2,2,2,2,8,8,2,2,2,2,2,2,8,2,2],[1,2,2,2,2,8,2,8,2,2,2,8,2,2,2,2],[1,4,2,2,4,4,1,1,2,8,8,4,1,4,1,2],[1,4,2,4,2,4,1,2,1,8,4,8,1,4,2,1],[1,4,4,2,2,4,2,1,1,8,4,4,2,8,1,1],[1,2,4,4,4,2,1,1,4,8,8,2,1,2,1,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,2,4,4,4,2,1,4,1,8,2,8,1,2,4,1],[1,1,4,2,8,1,2,4,1,8,4,4,2,2,4,1],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,2,4,4,4,2,4,1,1,8,2,2,4,8,1,1],[1,1,2,4,8,1,4,2,1,8,4,2,4,4,2,1],[1,1,2,8,4,1,4,1,2,8,2,4,4,4,1,2],[1,2,2,2,8,2,2,2,2,8,8,2,2,2,2,2],[1,2,8,2,2,2,2,2,2,8,2,2,2,8,2,2],[1,2,2,8,2,2,2,2,2,8,2,8,2,2,2,2]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

30 435 3194 11127 19586 17694 7728 1282

polytope > print \$p->VERTICES_IN_FACETS;

{0 1 2 6 7 8 15 16 17 21 22 23}
{0 1 2 9 10 11 15 16 17 24 25 26}
{0 1 2 3 4 5 15 16 17 18 19 20}
{5 8 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{7 10 12 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{10 11 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{4 5 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{7 8 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{4 11 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29}
{1 2 6 9 13 14 16 17 21 24 28 29}
{1 2 4 5 13 14 16 17 19 20 28 29}
{1 2 6 8 13 16 17 21 23 28}
{9 10 11 16 17 21 22 24 25}
{1 2 9 11 14 16 17 24 26 29}
{0 1 2 5 8 13 15 16 17 20 23 28}
{0 1 10 11 15 16 17 20 23 28}
{1 2 6 7 9 10 16 17 21 22 24 25}
{6 7 8 16 17 21 22 24 25}
{0 1 2 4 11 14 15 16 17 19 26 29}
{0 2 7 8 15 16 17 19 26 29}
{0 1 2 7 10 12 15 16 17 22 25 27}
{1 2 4 5 15 16 17 22 25 27}
{4 5 13 14 16 17 21 24 28 29}
{2 8 13 16 17 19 20 28 29}
{2 5 13 15 17 22 23 27 28}
{2 7 8 16 17 19 20 28 29}
{1 2 7 10 16 17 19 20 28 29}
{1 2 6 7 9 10 16 17 28 29}
{0 2 9 10 12 17 22 27 28}
{0 2 3 9 12 13 15 17 18 24 27 28}
{7 9 10 17 21 22 23 24 28}
{9 10 11 17 21 22 23 24 28}
{2 6 7 8 9 13 17 24 28 29}
{7 8 13 17 19 24 26 28 29}
{4 5 13 17 21 22 23 24 28}
{4 13 14 17 21 22 23 24 28}
{0 2 9 10 12 15 17 24 25 27}
{9 10 11 17 22 24 25 27 28}
{6 7 9 10 16 17 21 24 28 29}
{7 8 13 17 22 24 25 27 28}
{2 3 4 5 9 13 17 18 19 20 24 28}
{7 12 13 17 18 19 20 24 28}
{2 4 9 11 13 14 17 19 24 26 28 29}
{4 9 11 17 22 24 25 27 28}
{7 8 13 17 18 19 20 24 28}
{2 6 7 8 9 13 17 21 22 23 24 28}
{2 4 9 11 13 14 17 22 24 28}
{9 10 12 17 18 19 20 24 28}
{2 7 9 10 12 13 17 19 24 28}
{4 5 13 14 16 17 21 22 24 25}
{9 11 14 17 21 22 23 24 28}
{0 2 3 5 13 15 17 18 20 28}
{9 10 11 17 19 24 26 28 29}
{2 3 4 5 9 13 17 24 27 28}
{1 2 9 11 14 17 19 28 29}
{2 4 9 13 17 22 24 25 27 28}
{0 2 3 4 9 11 15 17 18 19 24 26}
{0 2 7 8 12 13 15 17 22 23 27 28}
{2 9 12 13 17 18 19 20 24 28}
{7 9 10 17 19 24 26 28 29}
{2 4 13 14 16 17 24 26 29}
{4 9 11 17 18 19 20 24 28}
{2 9 13 14 17 21 22 23 24 28}
{9 10 11 17 18 19 20 24 28}
{2 7 12 13 15 17 24 25 27}
{4 5 13 17 22 24 25 27 28}
{4 5 13 17 19 24 26 28 29}
{0 1 2 4 11 14 15 17 22 23}
{3 4 5 15 17 18 19 24 26}
{9 10 11 15 17 18 19 24 26}
{0 8 13 15 16 17 18 19 20}
{0 2 13 15 16 17 18 19 20}
{0 7 8 15 16 17 18 19 20}
{2 5 13 15 17 18 19 24 26}
{2 3 5 15 17 18 19 24 26}
{9 10 11 15 17 18 24 27 28}
{0 7 12 15 16 17 18 19 20}
{0 2 7 8 12 13 15 17 19 26}
{2 8 13 16 17 21 22 24 25}
{2 6 8 16 17 21 22 24 25}
{7 8 12 13 15 17 18 19 24 26}
{0 10 12 15 17 22 23 27 28}
{3 4 5 15 17 18 24 27 28}
{0 2 12 13 15 17 18 19 24 26}
{0 2 4 11 15 17 22 23 27 28}
{0 2 3 4 9 11 15 17 27 28}
{1 11 14 16 17 19 20 28 29}
{1 4 14 15 16 17 20 23 28}
{1 10 11 16 17 19 20 28 29}
{1 11 14 15 16 17 20 23 28}
{2 4 5 15 17 22 23 27 28}
{6 7 8 16 17 21 24 28 29}
{3 4 9 11 15 17 18 24 27 28}
{9 10 12 15 17 18 24 27 28}
{3 5 13 15 17 18 24 27 28}
{7 8 12 13 15 17 18 24 27 28}
{0 7 8 15 16 17 20 23 28}
{0 7 12 15 16 17 20 23 28}
{1 4 5 15 16 17 20 23 28}
{0 10 11 15 17 22 23 27 28}
{2 7 9 13 17 19 24 26 28 29}
{0 10 12 15 16 17 20 23 28}
{1 11 14 16 17 21 22 24 25}
{0 10 12 15 17 18 19 24 26}
{0 9 10 15 17 18 19 24 26}
{1 9 11 16 17 21 22 24 25}
{0 10 12 15 16 17 24 25 26}
{2 8 13 15 16 17 22 25 27}
{9 11 14 16 17 21 24 28 29}
{6 8 13 16 17 21 24 28 29}
{2 7 8 15 16 17 22 25 27}
{9 10 11 16 17 21 24 28 29}
{2 8 13 15 16 17 21 22 23}
{1 2 13 15 16 17 21 22 23}
{2 7 9 10 12 13 17 22 24 25 27 28}
{2 5 13 15 16 17 22 25 27}
{0 1 14 15 16 17 18 19 20}
{1 4 14 15 16 17 18 19 20}
{2 4 5 15 16 17 19 26 29}
{2 5 13 15 16 17 19 26 29}
{2 5 13 15 16 17 18 19 20}
{2 8 13 15 16 17 19 26 29}
{0 1 12 15 16 17 21 22 23}
{2 5 13 15 16 17 24 25 26}
{2 4 5 15 16 17 24 25 26}
{2 7 8 15 16 17 24 25 26}
{2 8 13 15 16 17 24 25 26}
{2 7 12 15 16 17 24 25 26}
{2 4 14 15 16 17 24 25 26}
{0 10 11 15 16 17 19 26 29}
{1 2 13 14 16 17 21 22 24 25}
{0 10 12 15 16 17 19 26 29}
{1 4 14 15 16 17 21 22 23}
{1 4 5 15 16 17 21 22 23}
{1 11 14 15 16 17 21 22 23}
{1 10 11 15 16 17 21 22 23}
{1 10 12 15 16 17 21 22 23}
{0 10 11 15 16 17 18 19 20}
{1 5 13 15 16 17 21 22 23}
{0 11 14 15 16 17 18 19 20}
{0 7 12 15 16 17 19 26 29}
{0 1 2 7 10 12 16 17 19 20}
{0 7 12 15 16 17 21 22 23}
{1 11 14 15 16 17 24 25 26}
{1 2 14 15 16 17 24 25 26}
{1 2 4 5 13 14 16 17 22 25}
{0 10 12 15 16 17 18 19 20}
{1 10 11 15 16 17 22 25 27}
{1 11 14 15 16 17 22 25 27}
{1 4 14 15 16 17 22 25 27}
{0 2 12 15 16 17 24 25 26}
{3 5 7 8 12 18 19 27}
{4 5 14 21 22 25 26 29}
{4 5 6 8 14 22 25 29}
{3 9 10 11 18 20 27 28}
{3 4 11 15 18 20 23 27 28}
{6 7 8 16 18 19 20 21 29}
{7 10 11 14 19 21 22 29}
{7 10 12 14 19 21 22 29}
{5 9 10 11 22 25 27 28}
{0 2 3 5 13 18 19 20}
{6 7 12 16 18 19 20 21 29}
{10 11 12 15 18 20 23 27 28}
{3 4 7 12 19 25 26 27}
{3 4 5 7 19 25 26 27}
{3 5 7 12 19 25 26 27}
{6 8 11 14 21 22 25 26}
{3 7 8 12 19 26 27 29}
{3 5 7 8 19 26 27 29}
{6 7 8 16 21 22 25 27 29}
{1 4 5 14 16 20 23 28}
{7 8 9 10 13 24 25 26}
{10 11 12 14 18 19 21 22 27 29}
{3 5 10 12 20 22 23 27}
{3 4 5 10 20 22 23 27}
{3 4 10 12 20 22 23 27}
{1 5 6 8 13 14 16 21 25 29}
{5 8 12 13 18 19 20 25}
{5 7 8 12 18 19 20 25}
{0 3 11 12 15 18 20 23 27 28}
{5 8 12 13 18 19 25 26}
{4 5 9 11 13 19 20 24 26 28}
{3 4 10 11 12 22 23 27}
{4 5 9 11 13 24 25 26}
{0 3 5 8 12 13 15 18 26 27}
{0 3 9 10 11 12 18 20 28}
{7 8 9 10 23 24 26 28}
{3 4 5 7 19 26 27 29}
{3 4 7 12 19 26 27 29}
{0 3 9 10 11 12 23 27 28}
{4 5 13 14 21 23 24 26 28 29}
{9 10 11 22 23 24 25 28}
{6 7 14 19 20 21 23 29}
{3 4 6 7 12 14 18 19 21 22 27 29}
{3 4 10 11 18 20 25 27}
{3 9 10 11 18 20 25 27}
{6 7 8 19 20 21 23 29}
{6 7 8 9 23 24 26 28}
{5 8 12 13 18 20 25 27}
{5 7 8 12 18 20 25 27}
{7 10 11 14 19 21 22 23}
{6 7 10 11 20 23 28 29}
{1 3 4 5 6 14 20 21 23}
{7 10 12 14 19 21 22 23}
{6 10 11 14 20 23 28 29}
{7 10 12 14 19 20 21 23}
{1 6 7 10 16 20 21 23}
{0 3 6 7 8 12 26 27 29}
{0 3 5 8 12 13 18 19 20}
{4 5 6 8 14 25 26 29}
{3 4 9 11 18 20 24 25 27 28}
{0 3 6 7 8 12 18 19 20}
{1 6 10 14 16 20 21 23 28 29}
{2 6 7 8 9 13 24 26 29}
{4 5 7 8 19 22 25 26 27 29}
{6 7 8 9 10 11 21 22 23 24 25 26}
{3 5 9 10 12 13 18 20 24 25 27 28}
{4 11 12 14 18 22 23 27}
{3 4 12 14 18 22 23 27}
{7 8 12 13 18 20 24 25 27 28}
{6 7 10 11 14 20 23 29}
{1 6 7 10 12 14 20 21 23}
{4 6 7 8 22 25 26 29}
{6 8 9 11 13 14 24 25 26}
{3 5 7 8 12 18 20 22 23 27}
{4 6 7 14 22 25 26 29}
{3 4 7 12 18 21 22 23}
{0 2 3 5 13 15 23 27 28}
{4 6 8 14 22 25 26 29}
{3 4 5 15 18 20 23 27 28}
{1 6 13 14 16 21 24 25 26 29}
{4 5 8 19 21 22 23 26 29}
{3 5 9 10 12 13 18 19 20}
{3 5 9 10 12 13 24 25 26}
{4 5 14 16 20 21 23 28 29}
{4 5 13 22 23 24 25 28}
{3 4 6 7 12 14 18 19 20}
{7 10 11 14 19 20 23 29}
{7 8 10 13 20 24 25 28}
{7 8 9 10 13 22 23 24 25 28}
{7 10 11 19 21 22 23 26 29}
{3 4 10 11 12 18 19 25 26 27}
{3 5 9 10 12 13 18 19 24 26}
{3 4 5 6 7 8 19 22 27 29}
{7 8 10 13 20 24 26 28}
{7 10 12 13 19 20 24 28}
{3 5 10 12 18 24 25 26}
{3 4 5 15 18 19 26 27 29}
{3 5 8 15 18 19 26 27 29}
{7 8 12 15 18 19 26 27 29}
{11 12 14 15 18 21 22 23 27}
{5 8 9 10 11 13 20 23 24 25 26 28}
{3 5 7 8 12 18 19 20}
{0 3 4 11 12 14 18 19 20}
{7 10 13 19 20 24 26 28}
{2 6 7 8 9 13 19 28 29}
{6 7 9 10 21 23 24 26 28 29}
{3 4 10 11 12 18 19 20}
{7 10 12 13 20 24 25 28}
{1 6 7 12 16 20 21 23}
{1 5 6 8 13 14 21 22 23}
{0 3 9 10 11 12 18 19 20}
{1 6 7 10 12 14 21 22 23}
{3 4 5 15 16 18 19 29}
{1 6 9 10 11 14 21 23 28}
{1 6 9 10 11 14 21 22 23}
{4 5 9 11 13 22 23 28}
{1 3 4 5 6 14 21 22 23}
{1 6 9 10 11 14 21 22 25}
{7 8 9 10 13 19 20 28}
{4 5 14 16 21 22 25 27 29}
{0 3 9 10 11 12 22 23 27}
{8 9 11 13 19 20 26 28}
{3 5 12 13 18 24 25 26}
{8 9 10 11 19 20 26 28}
{3 6 7 8 18 19 22 27}
{3 5 7 8 18 19 22 27}
{8 9 10 13 19 20 26 28}
{2 3 4 5 9 13 19 24 26}
{3 6 7 8 18 19 27 29}
{0 11 12 14 16 18 19 20}
{4 5 13 14 21 22 23 24 25 26}
{6 7 8 18 19 21 22 27 29}
{7 8 10 13 20 24 25 26}
{7 10 12 13 19 20 24 26}
{5 8 12 18 19 25 26 27}
{5 7 8 12 18 19 25 27}
{7 8 12 18 19 25 26 27}
{7 10 12 13 20 24 25 26}
{4 5 8 11 13 14 19 20 23 26 28 29}
{3 5 6 8 18 19 21 22 27 29}
{6 7 9 10 16 24 26 29}
{5 6 8 16 21 22 25 27 29}
{5 7 8 10 12 13 20 22 23 25 27 28}
{3 4 5 9 10 11 20 25 27 28}
{5 8 9 10 11 13 19 20 26}
{10 12 14 16 18 19 20 21 29}
{2 4 9 11 13 14 24 25 26}
{4 5 9 11 13 22 25 28}
{2 7 9 10 12 13 24 25 26}
{3 4 14 15 18 21 22 23 27}
{3 4 5 15 18 21 22 23 27}
{2 6 7 8 9 13 24 25 26}
{4 5 6 14 21 22 27 29}
{10 11 12 15 18 21 22 23 27}
{3 4 11 12 18 20 23 27}
{5 6 8 14 21 22 25 29}
{4 5 6 8 14 21 22 29}
{10 11 12 18 20 22 23 27}
{4 11 12 18 20 22 23 27}
{4 10 11 12 18 20 22 27}
{7 10 12 14 19 20 21 29}
{2 3 4 5 9 13 24 25 26}
{3 4 5 18 19 21 22 27 29}
{6 7 12 14 19 20 21 29}
{10 11 14 16 18 19 20 21 29}
{6 9 10 11 21 23 28 29}
{0 1 3 6 12 14 18 19 20}
{7 8 10 13 19 20 26 28}
{6 9 10 11 21 23 26 29}
{6 7 10 11 21 23 26 29}
{0 1 3 6 12 14 21 22 23}
{4 9 11 13 22 24 25 28}
{1 5 6 8 13 14 16 20 21 23 28 29}
{3 10 11 12 18 20 27 28}
{6 8 13 14 21 25 26 29}
{0 3 4 11 12 14 18 20 23}
{5 8 13 14 21 25 26 29}
{3 4 10 11 12 18 20 27}
{2 3 4 5 9 13 22 27 28}
{0 3 6 7 8 12 15 18 27 29}
{2 4 9 11 13 14 22 23 28}
{0 3 8 12 15 18 19 26 27 29}
{3 4 12 18 20 22 23 27}
{3 4 5 18 20 22 23 27}
{0 1 3 6 12 14 21 22 27}
{0 1 3 6 12 14 18 20 21 23}
{2 7 9 10 12 13 22 23 28}
{5 6 8 16 18 19 20 21 29}
{3 7 8 12 18 19 27 29}
{6 7 10 16 20 21 23 28 29}
{0 1 3 6 12 14 18 19 29}
{3 5 12 18 19 25 26 27}
{3 4 5 18 19 25 26 27}
{0 10 11 12 16 18 19 20}
{7 9 10 13 19 24 26 28}
{10 11 14 16 20 21 23 28 29}
{4 5 8 11 13 14 22 23 25 26}
{2 3 4 5 9 13 22 23 28}
{4 5 11 13 22 23 25 28}
{4 5 9 13 24 25 27 28}
{6 7 8 16 21 24 25 26 29}
{2 4 9 11 13 14 19 20 28}
{7 8 13 19 20 24 26 28}
{3 4 5 9 24 25 27 28}
{1 10 11 14 16 21 23 28}
{4 5 10 11 20 22 23 25 27 28}
{3 5 8 15 18 21 22 23 27}
{3 4 12 14 18 21 22 23}
{3 5 9 10 12 13 22 23 27 28}
{2 7 9 10 12 13 19 20 28}
{2 6 7 8 9 13 19 20 28}
{6 8 13 16 21 24 25 26 29}
{3 4 6 7 12 14 18 20 21 23}
{0 1 3 4 14 18 19 20}
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{0 1 10 12 16 17 20 28}
{0 1 10 12 16 17 23 28}
{0 2 10 12 17 22 23 28}
{0 2 9 10 17 22 23 28}
{0 1 6 8 16 17 23 28}
{0 1 6 7 16 17 23 28}
{0 1 7 12 16 17 20 28}
{0 1 7 12 16 17 23 28}
{0 2 8 13 15 16 17 19}
{0 1 2 7 16 17 20 28}
{0 1 2 6 7 8 16 17 28}
{0 2 7 8 16 17 20 28}
{0 2 10 12 16 17 24 25}
{0 2 10 12 16 17 24 26}
{1 2 9 10 17 19 20 28}
{2 7 9 10 17 19 28 29}
{1 2 9 10 17 19 28 29}
{2 9 10 16 17 24 26 29}
{2 7 10 16 17 24 26 29}
{2 7 9 10 17 24 26 29}
{2 7 9 10 16 17 24 29}
{0 1 4 14 15 17 18 20}
{1 9 11 14 16 17 21 24}
{9 10 11 16 17 24 26 29}
{0 7 8 12 15 17 18 20}
{0 8 12 13 15 17 18 19}
{0 9 10 11 15 17 18 19}
{0 9 10 11 15 17 19 26}
{0 7 8 12 15 17 18 19}
{0 4 11 14 15 17 18 20}
{1 4 5 14 16 17 21 22}
{2 6 7 8 16 17 28 29}
{2 3 4 5 15 17 24 27}
{2 4 5 15 17 24 25 27}
{2 3 4 9 15 17 24 27}
{2 3 5 13 15 17 24 27}
{2 5 13 15 17 24 25 27}
{2 3 4 5 15 17 24 26}
{2 7 8 13 15 17 24 25}
{2 7 8 13 15 17 24 26}
{1 2 9 14 17 21 22 23}
{1 2 13 14 17 21 22 23}
{2 7 12 13 15 17 24 26}
{2 4 11 14 15 17 24 25}
{2 4 11 14 15 17 24 26}
{1 2 13 14 17 21 23 28}
{1 2 9 14 17 21 23 28}
{1 2 6 9 17 21 23 28}
{1 2 9 14 17 21 22 24}
{1 2 9 14 17 22 24 25}
{4 5 13 16 17 24 26 29}
{7 8 12 15 17 18 20 28}
{0 1 7 12 16 17 21 22}
{7 8 13 15 17 24 25 27}
{1 4 5 14 16 17 21 23}
{0 2 9 10 12 17 24 26}
{0 2 7 8 12 13 17 19 20}
{0 1 2 4 11 14 17 19 20}
{0 2 9 10 12 17 19 20}
{0 1 2 9 10 11 17 19 20}
{1 2 9 11 14 17 22 23}
{1 2 4 5 13 14 17 22 23}
{0 1 2 9 10 11 17 22 23}
{0 1 2 7 10 12 17 22 23}
{0 10 12 15 17 18 20 28}
{0 10 11 15 17 18 20 28}
{2 6 7 9 16 17 24 29}
{2 4 9 11 17 18 19 20}
{0 2 9 11 17 18 19 20}
{0 2 4 11 17 18 19 20}
{0 2 3 4 9 11 17 18 20}
{1 2 4 5 13 14 17 23 28}
{1 2 9 11 14 17 23 28}
{0 1 2 7 10 12 17 20 28}
{0 1 2 9 10 11 17 20 28}
{0 1 2 6 7 8 17 23 28}
{0 1 2 7 10 12 17 23 28}
{1 2 6 7 9 10 17 23 28}
{0 1 2 4 11 14 17 23 28}
{0 2 7 8 12 13 17 20 28}
{0 1 2 3 4 5 17 20 28}
{0 1 2 9 10 11 17 23 28}
{0 1 2 4 11 14 17 20 28}
{0 2 9 10 12 17 20 28}
{0 2 3 4 9 11 17 20 28}
{1 2 11 14 15 17 24 25}
{1 2 11 14 15 17 24 26}
{0 1 7 12 16 17 21 23}
{2 6 7 8 16 17 24 29}
{2 7 8 16 17 24 26 29}
{0 2 12 13 17 18 20 28}
{0 2 9 12 17 18 20 28}
{0 2 3 9 17 18 20 28}
{0 1 10 11 15 17 22 27}
{1 2 4 14 15 17 25 27}
{1 2 11 14 15 17 25 27}
{2 4 11 14 15 17 25 27}
{0 2 9 10 12 17 19 26}
{2 7 9 10 17 19 26 29}
{2 4 5 13 17 19 26 29}
{2 7 8 13 17 19 26 29}
{2 7 10 12 17 19 26 29}
{0 1 2 9 10 11 17 19 29}
{0 2 9 11 17 19 26 29}
{0 2 9 10 17 19 26 29}
{0 2 7 12 17 19 26 29}
{0 2 10 12 17 19 26 29}
{0 9 10 11 17 19 26 29}
{0 1 2 9 10 11 15 17 27}
{1 2 9 11 15 17 25 27}
{1 2 9 10 15 17 25 27}
{1 9 10 11 15 17 25 27}
{2 7 8 13 15 17 25 27}
{0 1 2 11 15 17 22 27}
{1 2 4 14 15 17 22 27}
{1 2 11 14 15 17 22 27}
{2 4 11 14 15 17 22 27}
{2 6 8 13 16 17 21 24}
{2 7 8 13 17 22 25 27}
{2 4 9 11 17 22 25 27}
{1 2 9 11 14 17 22 25}
{2 4 5 13 17 22 25 27}
{0 1 2 9 10 11 17 22 27}
{1 2 4 14 17 22 25 27}
{1 2 11 14 17 22 25 27}
{2 4 11 14 17 22 25 27}
{1 2 9 11 17 22 25 27}
{1 2 9 10 17 22 25 27}
{1 9 10 11 17 22 25 27}
{2 3 4 5 15 17 27 28}
{2 3 4 5 15 17 19 26}
{1 2 9 10 17 21 22 23}
{2 7 9 10 17 21 22 23}
{1 2 6 7 9 10 17 21 23}
{1 2 7 10 17 21 22 23}
{2 3 5 13 15 17 18 24}
{0 3 4 11 15 17 18 28}
{0 3 4 15 17 18 20 28}
{0 4 11 15 17 18 20 28}
{0 3 4 11 17 18 20 28}
{2 6 8 13 16 17 24 29}
{2 8 13 16 17 24 26 29}
{0 1 10 11 15 17 22 23}
{0 1 10 12 15 17 22 23}
{1 6 7 10 17 21 23 28}
{1 7 10 16 17 21 23 28}
{1 6 7 16 17 21 23 28}
{1 6 7 10 16 17 21 28}
{1 2 4 5 15 17 22 23}
{1 2 5 13 15 17 22 23}
{6 7 8 16 17 21 23 28}
{2 4 9 11 17 22 27 28}
{0 2 9 11 17 22 27 28}
{0 2 9 11 17 22 23 28}
{0 4 11 14 15 17 18 19}
{1 5 13 14 16 17 21 22}
{0 9 10 12 15 17 18 24}
{9 10 11 15 17 24 25 27}
{0 1 3 5 15 17 20 28}
{1 9 11 14 17 21 22 24}
{1 9 11 14 17 22 24 25}
{7 8 12 13 17 18 19 20}
{0 4 11 14 15 17 23 28}
{0 4 11 14 15 17 20 28}
{1 3 4 5 15 17 20 28}
{0 1 3 4 15 17 20 28}
{0 7 8 12 15 17 20 28}
{0 2 12 13 17 18 19 20}
{0 2 9 12 17 18 19 20}
{0 2 9 12 17 19 24 26}
{0 2 9 12 17 18 19 24}
{0 9 10 12 15 17 18 28}
{0 3 9 11 15 17 18 28}
{0 9 10 12 15 17 27 28}
{0 9 10 11 15 17 18 28}
{0 9 10 11 15 17 27 28}
{0 1 11 14 15 17 23 28}
{0 1 11 14 15 17 20 28}
{1 9 10 11 17 19 28 29}
{1 9 10 11 17 19 20 28}
{0 1 4 14 15 17 23 28}
{0 1 4 14 15 17 20 28}
{0 1 2 4 15 17 23 28}
{0 1 2 3 4 5 15 17 28}
{1 2 4 5 15 17 23 28}
{0 1 7 12 17 21 22 23}
{2 6 8 13 16 17 28 29}
{0 9 10 11 17 22 27 28}
{0 9 10 11 17 22 23 28}
{1 2 11 14 17 19 20 28}
{1 2 9 11 17 19 20 28}
{1 9 11 14 16 17 21 28}
{1 9 10 11 16 17 21 28}
{1 6 9 10 16 17 21 28}
{1 9 11 14 16 17 28 29}
{1 9 10 11 16 17 28 29}
{0 9 10 12 17 19 24 26}
{0 9 10 12 17 18 19 24}
{0 1 4 14 15 17 18 19}
{2 4 5 13 16 17 24 26}
{2 4 5 13 16 17 24 25}
{2 4 5 13 17 24 25 27}
{2 6 7 8 16 17 24 25}
{2 7 10 12 16 17 24 26}
{2 7 10 12 16 17 24 25}
{2 4 13 14 16 17 24 25}
{0 1 11 14 15 16 17 20}
{0 1 10 12 15 16 17 23}
{1 7 10 12 16 17 21 22}
{1 7 10 12 16 17 21 23}
{1 9 10 11 16 17 21 22}
{1 9 10 11 16 17 22 25}
{2 9 10 12 17 19 24 26}
{2 7 9 10 17 19 24 26}
{2 7 10 12 17 19 24 26}
{2 7 12 13 17 19 24 26}
{2 4 9 11 17 22 24 25}
{2 9 11 14 17 22 24 25}
{2 4 13 14 17 22 24 25}
{2 4 11 14 17 22 24 25}
{2 7 8 13 17 22 24 25}
{2 6 7 8 17 22 24 25}
{0 1 4 14 17 18 19 20}
{2 7 8 13 17 19 20 28}
{2 7 12 13 17 19 20 28}
{2 7 10 12 17 19 20 28}
{2 9 10 12 17 19 20 28}
{1 11 14 16 17 21 23 28}
{1 10 11 16 17 21 23 28}
{2 4 9 11 17 19 20 28}
{2 4 11 14 17 19 20 28}
{2 4 5 13 17 22 23 28}
{2 7 9 10 17 22 23 28}
{2 7 10 12 17 22 23 28}
{2 9 11 14 17 22 23 28}
{2 4 13 14 17 22 23 28}
{2 4 11 14 17 22 23 28}
{2 4 5 13 17 22 27 28}
{1 5 13 14 16 17 21 23 28}
{4 5 13 14 17 21 22 23}
{2 4 5 13 17 19 24 26}
{2 3 4 5 17 19 24 26}
{1 4 5 14 17 21 22 23}
{1 9 11 14 17 21 22 23}
{1 9 10 11 17 21 22 23}
{1 9 11 14 17 21 23 28}
{1 9 10 11 17 21 23 28}
{1 6 9 10 17 21 23 28}
{1 7 10 12 17 21 22 23}
{0 9 10 12 17 18 19 20}
{0 9 10 11 17 18 19 20}
{1 5 13 14 17 21 22 23}
{6 7 9 10 17 21 23 28}
{2 7 8 13 17 19 28 29}
{0 4 11 14 17 18 19 20}
{4 5 14 16 17 21 23 28}
{3 4 5 15 17 18 20 28}
{2 3 5 13 15 17 27 28}
{7 8 12 13 17 18 20 28}
{2 7 8 13 17 24 26 29}
{0 7 8 12 17 18 19 20}
{3 4 9 11 17 18 20 28}
{0 8 12 13 17 18 19 20}
{4 5 13 14 17 21 23 28}
{0 9 10 12 17 18 20 28}
{0 3 9 11 17 18 20 28}
{0 9 10 11 17 18 20 28}
{1 4 5 14 16 17 23 28}

-----------------------------------------------------------------------

Try the subfacet: {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 25 26}

\$points=new Matrix([[1,4,1,1,2,8,2,2,4,4,8,4,1,4,1,2],[1,4,1,2,1,8,2,4,2,4,4,8,1,4,2,1],[1,4,2,1,1,8,4,2,2,4,4,4,2,8,1,1],[1,2,1,1,4,8,4,4,4,2,8,2,1,2,1,4],[1,1,2,1,4,8,4,8,2,1,4,4,2,2,1,4],[1,1,1,2,4,8,8,4,2,1,4,2,1,4,2,4],[1,2,1,4,1,8,4,4,4,2,2,8,1,2,4,1],[1,1,2,4,1,8,4,2,8,1,4,4,2,2,4,1],[1,1,1,4,2,8,8,2,4,1,2,4,1,4,4,2],[1,2,4,1,1,8,4,4,4,2,2,2,4,8,1,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,4,1,2,8,2,8,4,1,2,4,4,4,1,2],[1,2,2,2,2,8,2,2,8,2,8,2,2,2,2,2],[1,2,2,2,2,8,8,2,2,2,2,2,2,8,2,2],[1,2,2,2,2,8,2,8,2,2,2,8,2,2,2,2],[1,1,2,4,8,1,4,2,1,8,4,2,4,4,2,1],[1,1,2,8,4,1,4,1,2,8,2,4,4,4,1,2]]);

polytope > \$p=new Polytope(POINTS=>\$points);

polytope > print \$p->F_VECTOR;

17 136 475 815 722 315 54

polytope > print \$p->VERTICES_IN_FACETS;

{0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15}
{0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16}
{2 7 9 10 12 13 15 16}
{2 3 4 5 9 13 15 16}
{2 6 7 8 9 13 15 16}
{2 4 9 11 13 14 15 16}
{0 1 2 9 10 11 15 16}
{0 1 2 4 11 14 15 16}
{0 2 3 4 9 11 15 16}
{0 2 7 8 12 13 15 16}
{0 2 3 9 12 13 15 16}
{0 1 2 6 7 8 15 16}
{0 1 2 3 4 5 15 16}
{1 2 6 7 9 10 15 16}
{1 2 6 9 13 14 15 16}
{1 2 4 5 13 14 15 16}
{0 1 2 5 8 13 15 16}
{0 1 2 7 10 12 15 16}
{4 5 6 8 14 15 16}
{0 3 4 11 12 14 15 16}
{7 8 9 10 13 15 16}
{1 6 7 10 12 14 15 16}
{0 3 9 10 11 12 15 16}
{4 6 7 8 11 14 15 16}
{3 4 6 7 12 14 15 16}
{6 8 9 11 13 14 15 16}
{1 3 4 5 6 14 15 16}
{4 5 8 11 13 14 15 16}
{1 5 6 8 13 14 15 16}
{4 5 7 8 10 11 15 16}
{0 3 5 8 12 13 15 16}
{1 6 9 10 11 14 15 16}
{4 5 9 11 13 15 16}
{0 1 10 11 12 14 15 16}
{0 1 3 5 6 8 15 16}
{0 1 3 6 12 14 15 16}
{3 4 5 7 10 12 15 16}
{5 8 9 10 11 13 15 16}
{3 5 9 10 12 13 15 16}
{3 5 7 8 12 15 16}
{0 1 3 4 14 15 16}
{0 1 6 7 12 15 16}
{3 4 5 6 7 8 15 16}
{4 7 10 11 12 14 15 16}
{5 7 8 10 12 13 15 16}
{6 7 8 9 10 11 15 16}
{6 7 10 11 14 15 16}
{3 4 10 11 12 15 16}
{3 4 5 9 10 11 15 16}
{0 3 6 7 8 12 15 16}
{1 2 9 11 14 15 16}
{0 2 3 5 13 15 16}
{1 2 6 8 13 15 16}
{0 2 9 10 12 15 16}