The stable-set bound for simple 4-polytopes with 8 facets:

  This file documents data for the article:
  Constantin Ickstadt, Thorsten Theobald and Bernhard von Stengel:
  A Stable-Set Bound and Maximal Numbers of Nash Equilibria in
  Bimatrix Games,
  arXiv:2411.12385 

  Link to accompanying Web page:
  https://www.math.uni-frankfurt.de/~ickstadt/nash-5x5/

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For each of the 37 simple 4-polytopes with 8 facets, the 
following table shows:
In column "No.": an ordering number from 0 to 36, the order of 
  the polytopes comes from the order in the data of Firsching's
  classification [1]. That classification uses the language
  of simplicial polytopes, which is dual to our setting.
  Note that the order of the polytopes does not coincide with
  the order in the classification of Gr"unbaum and Sreedharan [2]
  (which also uses the language of simplicial polytopes).
In column 2: the number of vertices of the simple 4-polytope with 
  8 facets
In column 3: twice the size of a largest stable set in the edge 
  graph
In column 4: the stable-set-bound

The maximal value which occurs in the fourth column table is 16 and 
the minimal value in that column is 8.

References:
[1] M. Firsching:
    https://ftp.imp.fu-berlin.de/pub/moritz/inscribe/neighborly/
    also available on firsching.ch
[2] B. Gr"unbaum, V. P. Sreedharan: An enumeration of simplicial
    4-polytopes with 8 vertices, J. Comb. Theory 2:437-465, 1967.

No. 2  3  4 
----------------------------------
 0 17 12 12
 1 18 14 12
 2 18 14 14
 3 18 14 12
 4 19 14 14
 5 17 12 12
 6 19 14 14
 7 16 12 10
 8 16 12 10
 9 16 12 12
10 17 12 12
11 19 14 14
12 18 14 12
13 16 12 10
14 15 10 10
15 20 14 14
16 18 14 14
17 19 14 14
18 17 12 12
19 20 16 16
20 20 16 16
21 18 14 12
22 17 14 14
23 16 16 16
24 17 12 12
25 17 12 12
26 17 14 12
27 15 10 10
28 16 10 10
29 16 12 12
30 15 10 10
31 15 10 10
32 15 10  8
33 16 12 12
34 14  8  8
35 14  8  8
36 14  8  8