P_3 = 1-2-3: edges 01 12; join: True; sets not contained in a join: 0, minimal: 
   false twin of 2: edges 01 03 12 23; join: True; sets not in a join: 0; minimal: ; all have r(Y) not in a join of Gamma: True
   true twin of 2: edges 01 03 12 13 23; join: True; sets not in a join: 0; minimal: ; all have r(Y) not in a join of Gamma: True
P_4 = 1-2-3-4: edges 01 12 23; join: False; sets not contained in a join: 4, minimal: {1,4}
   false twin of 1: edges 01 12 14 23; join: False; sets not in a join: 12; minimal: {1,4} {4,1'}; all have r(Y) not in a join of Gamma: True
   true twin of 1: edges 01 04 12 14 23; join: False; sets not in a join: 12; minimal: {1,4} {4,1*}; all have r(Y) not in a join of Gamma: True
   false twin of 2: edges 01 04 12 23 24; join: False; sets not in a join: 8; minimal: {1,4}; all have r(Y) not in a join of Gamma: True
   true twin of 2: edges 01 04 12 14 23 24; join: False; sets not in a join: 8; minimal: {1,4}; all have r(Y) not in a join of Gamma: True
pentagon (complement of the cycle 1-2-3-4-5): edges 02 03 13 14 24; join: False; sets not contained in a join: 11, minimal: {1,2,3} {2,3,4} {1,2,5} {1,4,5} {3,4,5}
   false twin of 1: edges 02 03 13 14 24 25 35; join: False; sets not in a join: 27; minimal: {1,2,3} {2,3,4} {1,2,5} {1,4,5} {3,4,5} {2,3,1'} {2,5,1'} {4,5,1'}; all have r(Y) not in a join of Gamma: True
   true twin of 1: edges 02 03 05 13 14 24 25 35; join: False; sets not in a join: 27; minimal: {1,2,3} {2,3,4} {1,2,5} {1,4,5} {3,4,5} {2,3,1*} {2,5,1*} {4,5,1*}; all have r(Y) not in a join of Gamma: True
