(*In this file, we go over all possible intersections of facets of a polytope in P^5 cut out by the coordiante hyperplanes and two additional hyperplanes h1 and h2 and check if a given intersection is a face or is in the residual arrangement*)
h1[x1_, x2_, x3_, x4_, x5_, x6_]:=x1+3*x2+x3+3*x4+x5-x6
h2[x1_, x2_, x3_, x4_, x5_, x6_]:=-4*x1-4*x2-x3-2*x4+2*x5+2*x6
(*Positroid cells*)

(*28 codim 2 pieces*)
1
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
2
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
3
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
4
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
5
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
6
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
7
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
8
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
9
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
10
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
11
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
12
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
13
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
14
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
15
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
16
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
17
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
18
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
19
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
20
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
21
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
22
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
23
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
24
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
25
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
26
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
27
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
28
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]

(*three hyperplanes*)

1
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
2
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
3
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
4
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
5
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
6
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
7
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
8
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
9
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
10
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
11
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
12
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
13
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
14
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
15
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
16
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
17
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
18
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
19
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
20
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
21
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
22
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
23
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
24
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
25
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
26
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
27
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
28
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
29
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
30
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
31
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
32
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
33
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
34
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
35
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
36
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
37
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
38
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
39
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
40
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
41
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
42
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
43
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
44
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
45
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
46
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
47
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
48
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
49
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
50
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
51
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
52
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
53
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
54
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
55
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
56
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]

(*Four hyperplanes: one-dimensional edges of the polytope*)

1
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
2
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
3
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
4
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
5
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
6
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
7
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
8
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
9
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
10
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
11
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
12
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
13
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
14
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
15
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*12 14 in the lead*)
16
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
17
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
18
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
19
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
20
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
21
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
22
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
23
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
24
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
25
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*12 23 in the lead*)
26 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
27
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
28
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
29 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
30
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
31
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*12 24 or 12 34 in the lead*)
32
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
33
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
34
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
35
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*13 14 in the lead*)
36
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
37
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
38
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
39
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
40
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
41
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
42
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
43
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
44
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
45
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*13 23 in the lead*)
46
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
47 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
48
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
49
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
50
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
51
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*13 24 or 13 34 in the lead*)
52
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
53
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
54
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
55
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*14 23 in the lead*)
56
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
57
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
58
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
59
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
60
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
61
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*14 24 or 14 34 in the lead*)
62
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
63
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
64
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
65
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
(*23 24 or 23 34 or 24 34 in the lead*)
66
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
67
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
68
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
69
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
70
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]

(*5 hyperplanes: isolated vertices of the polytope*)
(*12 in the lead*)
1
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
2
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
3
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
4
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
5
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
6
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
7
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
8 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
9
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
10 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
11
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
12
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
13
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
14
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
15
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
16
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
17
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
18
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
19
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
20
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
21
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14==0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
(*13 in the lead*)
22
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
23
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
24
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
25
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
26
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
27 
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
28
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
29
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
30
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
31
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
32
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
33
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
34
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
35
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
36
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14==0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
(*14 in the lead*)
37
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
38
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
39
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
40
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
41
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
42
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
43
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
44
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
45
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
46
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14>0 && p23==0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
(*23 in the lead*)
47
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
48
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
49
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
50
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
51
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
52
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23>0&&p24==0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
(*24 or 34 in the lead*)
53
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]
54
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
55
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23==0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
56
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13==0 && p14==0 && p23==0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]

Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12==0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13==0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0] ,Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14==0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23==0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24==0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34==0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]

Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]==0&&h2[p12,p13,p23,p14,p24,p34]>0],Reals]
Resolve[Exists[{p12,p13,p14,p23,p24,p34},p12>0&& p13>0 && p14>0 && p23>0&&p24>0&&p34>0&&h1[p12,p13,p23,p14,p24,p34]>0&&h2[p12,p13,p23,p14,p24,p34]==0],Reals]