Type I Trees for (aa2a3a4):

Line F23: 
[(set([E3, F14]), set([F45, F56, F16, F15, G3, E2, G2, F46])), (set([F45, F15]), set([F56, F16, G3, E3, E2, G2, F46, F14])), (set([F45, E3, F15, F14]), set([F56, F16, G3, E2, G2, F46])), (set([F45, E3, F15, F14, E2]), set([G2, F56, F46, F16, G3])), (set([G2, F56, F46, F16, G3]), set([F45, E3, F15, F14, E2])), (set([G2, F56, F46, F16]), set([F45, F15, G3, E3, E2, F14])), (set([G2, F56]), set([F45, F16, F15, G3, E3, E2, F46, F14])), (set([F46, F16]), set([F45, F56, F15, G3, E3, E2, G2, F14]))]
Line F36: 
[(set([E3, F14]), set([F45, F12, F15, G3, F25, F24, E6, G6])), (set([F45, F15]), set([F12, G3, F25, F24, E3, E6, G6, F14])), (set([F45, E3, F15, F14]), set([F12, G3, F25, F24, E6, G6])), (set([E6, E3, F15, F14, F45]), set([F12, F25, F24, G6, G3])), (set([F12, F25, F24, G6, G3]), set([E6, E3, F15, F14, F45])), (set([F12, F25, F24, G6]), set([F45, F15, G3, E3, E6, F14])), (set([F25, G6]), set([F45, F12, F15, G3, F24, E3, E6, F14])), (set([F12, F24]), set([F45, F15, G3, F25, E3, E6, G6, F14]))]
Line E1: 
[(set([F12, F16]), set([F15, G4, G3, G2, G6, G5, F14, F13])), (set([F15, G4]), set([F12, F16, G3, G2, G6, G5, F14, F13])), (set([F12, F16, F15, G4]), set([G3, G2, G6, G5, F14, F13])), (set([F12, F16, F15, G4, F13]), set([G2, G6, G5, F14, G3])), (set([G2, G6, G5, F14, G3]), set([F12, F16, F15, G4, F13])), (set([G2, G6, G5, F14]), set([F12, F16, F15, G4, G3, F13])), (set([G5, F14]), set([F12, F16, F15, G4, G3, G2, G6, F13])), (set([G2, G6]), set([F12, F16, F15, G4, G3, G5, F14, F13]))]
Line F12: 
[(set([G1, F45]), set([F36, E1, F56, E2, F35, F34, G2, F46])), (set([E1, F34]), set([F45, F36, G1, F56, E2, F35, G2, F46])), (set([G1, F45, E1, F34]), set([F36, F56, E2, F35, G2, F46])), (set([G1, F46, F45, E1, F34]), set([G2, F56, E2, F35, F36])), (set([G2, F56, E2, F35, F36]), set([G1, F46, F45, E1, F34])), (set([G2, F56, E2, F36]), set([F45, E1, G1, F35, F34, F46])), (set([E2, F36]), set([F45, E1, G1, F56, F35, F34, G2, F46])), (set([G2, F56]), set([F45, F36, E1, G1, E2, F35, F34, F46]))]
Line G4: 
[(set([E1, F34]), set([F45, F24, E3, E2, E6, E5, F46, F14])), (set([F24, F46]), set([F45, E1, E3, E2, F34, E6, E5, F14])), (set([F24, F46, E1, F34]), set([F45, E3, E2, E6, E5, F14])), (set([F24, F46, E5, E1, F34]), set([E6, F14, F45, E2, E3])), (set([E6, F14, F45, E2, E3]), set([F24, F46, E5, E1, F34])), (set([E6, E3, E2, F14]), set([F45, E1, F24, F34, E5, F46])), (set([E6, E2]), set([F45, E1, F24, E3, F34, E5, F46, F14])), (set([E3, F14]), set([F45, E1, F24, E2, F34, E6, E5, F46]))]
Line F25: 
[(set([F34, F13]), set([F36, F16, E2, G2, E5, F46, G5, F14])), (set([F34, G5, F14, F13]), set([F36, F16, E2, G2, E5, F46])), (set([E5, F34, G5, F14, F13]), set([G2, F46, F16, E2, F36])), (set([G2, F46, F16, E2, F36]), set([E5, F34, G5, F14, F13])), (set([F46, F16, E2, F36]), set([F34, G2, E5, G5, F14, F13])), (set([E2, F36]), set([F16, F34, G2, E5, F46, G5, F14, F13])), (set([F46, F16]), set([F36, E2, F34, G2, E5, G5, F14, F13]))]
Line E3: 
[(set([F34, F13]), set([F23, F36, G1, G4, F35, G2, G6, G5])), (set([G2, F34, G6, F13]), set([F23, F36, G1, G4, F35, G5])), (set([G2, F34, G6, F35, F13]), set([G1, F23, G5, G4, F36])), (set([G1, F23, G5, G4, F36]), set([G2, F34, G6, F35, F13])), (set([G1, F23, F36, G4]), set([F35, F34, G2, G6, G5, F13])), (set([G1, G4]), set([F23, F36, F35, F34, G2, G6, G5, F13])), (set([F23, F36]), set([G1, G4, F35, F34, G2, G6, G5, F13]))]
Line G2: 
[(set([F26, E3]), set([F23, E1, F12, E4, F25, F24, E6, E5])), (set([E4, E1]), set([F26, F23, F12, F25, F24, E3, E6, E5])), (set([F26, E4, E3, E1]), set([F23, F12, F25, F24, E6, E5])), (set([F26, E5, E4, E3, E1]), set([F12, F25, F24, F23, E6])), (set([F12, F25, F24, F23, E6]), set([F26, E5, E4, E3, E1])), (set([F12, E6, F24, F23]), set([F26, E1, E4, F25, E3, E5])), (set([F12, F24]), set([F26, F23, E1, E4, F25, E3, E6, E5])), (set([E6, F23]), set([F26, E1, F12, E4, F25, F24, E3, E5]))]
Line F13: 
[(set([G1, F45]), set([F26, E1, F56, G3, F25, F24, E3, F46])), (set([F24, F46]), set([F26, F45, E1, G1, F56, G3, F25, E3])), (set([G1, F24, F46, F45]), set([F26, E1, F56, G3, F25, E3])), (set([G1, F24, F46, F45, E1]), set([F26, F25, F56, E3, G3])), (set([F26, F25, F56, E3, G3]), set([G1, F24, F46, F45, E1])), (set([F26, F25, F56, E3]), set([F45, E1, G1, G3, F24, F46])), (set([F25, F56]), set([F26, F45, E1, G1, G3, F24, E3, F46])), (set([F26, E3]), set([F45, E1, G1, F56, G3, F25, F24, F46]))]
Line F45: 
[(set([F12, F16]), set([F26, F23, F36, E4, G4, E5, G5, F13])), (set([E4, F13]), set([F26, F23, F36, F12, F16, G4, E5, G5])), (set([F12, E4, F16, F13]), set([F26, F23, F36, G4, E5, G5])), (set([F12, E5, E4, F16, F13]), set([F26, F23, F36, G4, G5])), (set([F26, F23, F36, G4, G5]), set([F12, E5, E4, F16, F13])), (set([F26, F23, F36, G5]), set([F12, E4, F16, G4, E5, F13])), (set([F26, G5]), set([F23, F36, F12, E4, F16, G4, E5, F13])), (set([F23, F36]), set([F26, F12, E4, F16, G4, E5, G5, F13]))]
Line E4: 
[(set([G2, G6]), set([F45, G1, G3, F24, F34, F46, G5, F14])), (set([G2, G6, F14]), set([F45, G1, G3, F24, F34, F46, G5])), (set([G2, G6, G5, F14]), set([F45, G1, G3, F24, F34, F46])), (set([G2, G6, G5, F14, G3]), set([G1, F24, F46, F45, F34])), (set([G1, F24, F46, F45, F34]), set([G2, G6, G5, F14, G3])), (set([G1, F24, F46, F45]), set([G3, F34, G2, G6, G5, F14])), (set([G1, F24, F46]), set([F45, G3, F34, G2, G6, G5, F14])), (set([F24, F46]), set([F45, G1, G3, F34, G2, G6, G5, F14]))]
Line F24: 
[(set([F15, G4]), set([F36, F56, E4, F16, E2, F35, G2, F13])), (set([E4, F15, G4, F13]), set([F36, F56, F16, E2, F35, G2])), (set([E4, F16, F15, G4, F13]), set([G2, F56, E2, F35, F36])), (set([G2, F56, E2, F35, F36]), set([E4, F16, F15, G4, F13])), (set([G2, F56, E2, F36]), set([E4, F16, F15, G4, F35, F13])), (set([E2, F36]), set([F56, E4, F16, F15, G4, F35, G2, F13])), (set([G2, F56]), set([F36, E4, F16, F15, G4, E2, F35, F13]))]
Line E2: 
[(set([F12, F24]), set([F26, F23, G1, G4, G3, F25, G6, G5])), (set([F12, F25, F24, G6]), set([F26, F23, G1, G4, G3, G5])), (set([F12, F25, F24, G6, G3]), set([F26, G1, F23, G5, G4])), (set([F26, G1, F23, G5, G4]), set([F12, F25, F24, G6, G3])), (set([F26, G1, G5, G4]), set([F23, F12, G3, F25, F24, G6])), (set([G1, G4]), set([F26, F23, F12, G3, F25, F24, G6, G5])), (set([F26, G5]), set([F23, F12, G1, G4, G3, F25, F24, G6]))]
Line F46: 
[(set([E4, F13]), set([F23, F12, F15, G4, F25, F35, E6, G6])), (set([F15, G4]), set([F23, F12, E4, F25, F35, E6, G6, F13])), (set([E4, F15, G4, F13]), set([F23, F12, F25, F35, E6, G6])), (set([F12, E4, F15, G4, F13]), set([F25, F23, G6, F35, E6])), (set([F25, F23, G6, F35, E6]), set([F12, E4, F15, G4, F13])), (set([F25, F23, G6, E6]), set([F12, E4, F15, G4, F35, F13])), (set([E6, F23]), set([F12, E4, F15, G4, F25, F35, G6, F13])), (set([F25, G6]), set([F23, F12, E4, F15, G4, F35, E6, F13]))]
Line G6: 
[(set([E4, E1]), set([F26, F36, F56, F16, E3, E2, E5, F46])), (set([F26, E3]), set([F36, E1, F56, E4, F16, E2, E5, F46])), (set([F26, E4, E3, E1]), set([F36, F56, F16, E2, E5, F46])), (set([F26, E5, E4, E3, E1]), set([F56, F46, F16, E2, F36])), (set([F56, F46, F16, E2, F36]), set([F26, E5, E4, E3, E1])), (set([F46, F16, E2, F36]), set([F26, E1, F56, E4, E3, E5])), (set([E2, F36]), set([F26, E1, F56, E4, F16, E3, E5, F46])), (set([F46, F16]), set([F26, F36, E1, F56, E4, E3, E2, E5]))]
Line G5: 
[(set([E4, E1]), set([F45, F56, F15, F25, E3, E2, F35, E6])), (set([F25, F56]), set([F45, E1, E4, F15, E3, E2, F35, E6])), (set([F25, F56, E4, E1]), set([F45, F15, E3, E2, F35, E6])), (set([F25, F56, E4, E1, F35]), set([F45, E6, E3, F15, E2])), (set([F45, E6, E3, F15, E2]), set([F25, F56, E4, E1, F35])), (set([E6, F45, F15, E2]), set([E1, F56, E4, F25, E3, F35])), (set([E6, E2]), set([F45, E1, F56, E4, F15, F25, E3, F35])), (set([F45, F15]), set([E1, F56, E4, F25, E3, E2, F35, E6]))]
Line F14: 
[(set([F25, F56]), set([F26, F23, F36, E1, G1, E4, G4, F35])), (set([E4, E1]), set([F26, F23, F36, G1, F56, G4, F25, F35])), (set([F25, F56, E4, E1]), set([F26, F23, F36, G1, G4, F35])), (set([F25, F56, E4, E1, F35]), set([F26, G1, F23, F36, G4])), (set([F26, G1, F23, F36, G4]), set([F25, F56, E4, E1, F35])), (set([G1, F23, F36, G4]), set([F26, E1, F56, E4, F25, F35])), (set([G1, G4]), set([F26, F23, F36, E1, F56, E4, F25, F35])), (set([F23, F36]), set([F26, E1, G1, F56, E4, G4, F25, F35]))]
Line F26: 
[(set([F34, F13]), set([F45, F15, E2, F35, G2, E6, G6, F14])), (set([G2, F34, G6, F13]), set([F45, F15, E2, F35, E6, F14])), (set([G2, F34, G6, F35, F13]), set([E6, F45, F15, F14, E2])), (set([E6, F45, F15, F14, E2]), set([G2, F34, G6, F35, F13])), (set([E6, F45, F15, E2]), set([F35, F34, G2, G6, F14, F13])), (set([E6, E2]), set([F45, F15, F35, F34, G2, G6, F14, F13])), (set([F45, F15]), set([E2, F35, F34, G2, E6, G6, F14, F13]))]
Line F34: 
[(set([F26, E3]), set([F12, F56, E4, F16, F15, G4, G3, F25])), (set([F26, F25, F56, E3]), set([F12, E4, F16, F15, G4, G3])), (set([F26, F25, F56, E3, G3]), set([F12, E4, F16, F15, G4])), (set([F12, E4, F16, F15, G4]), set([F26, F25, F56, E3, G3])), (set([F12, F16, F15, G4]), set([F26, F56, E4, G3, F25, E3])), (set([F12, F16]), set([F26, F56, E4, F15, G4, G3, F25, E3])), (set([F15, G4]), set([F26, F12, F56, E4, F16, G3, F25, E3]))]
Line E6: 
[(set([F46, F16]), set([F26, F36, G1, F56, G4, G3, G2, G5])), (set([G2, F56]), set([F26, F36, G1, F16, G4, G3, F46, G5])), (set([F26, G5]), set([F36, G1, F56, F16, G4, G3, G2, F46])), (set([G1, G4]), set([F26, F36, F56, F16, G3, G2, F46, G5])), (set([G2, F56, F36]), set([F26, G1, F16, G4, G3, F46, G5])), (set([F26, G5, G3]), set([F36, G1, F56, F16, G4, G2, F46])), (set([G2, F56, F46, F16, F36]), set([F26, G1, G5, G4, G3])), (set([F26, G1, G5, G4, G3]), set([G2, F56, F46, F16, F36]))]
Line G1: 
[(set([E4, F13]), set([F12, F16, F15, E3, E2, E6, E5, F14])), (set([F12, F16]), set([E4, F15, E3, E2, E6, E5, F14, F13])), (set([F12, E4, F16, F13]), set([F15, E3, E2, E6, E5, F14])), (set([F12, E5, E4, F16, F13]), set([E6, E3, F15, F14, E2])), (set([E6, E3, F15, F14, E2]), set([F12, E5, E4, F16, F13])), (set([E6, E3, E2, F14]), set([F12, E4, F16, F15, E5, F13])), (set([E6, E2]), set([F12, E4, F16, F15, E3, E5, F14, F13])), (set([E3, F14]), set([F12, E4, F16, F15, E2, E6, E5, F13]))]
Line F56: 
[(set([G5, F14]), set([F23, F12, F24, F34, E6, E5, G6, F13])), (set([F34, F13]), set([F23, F12, F24, E6, E5, G6, G5, F14])), (set([F34, G5, F14, F13]), set([F23, F12, F24, E6, E5, G6])), (set([E5, F34, G5, F14, F13]), set([F12, E6, F24, F23, G6])), (set([F12, E6, F24, F23, G6]), set([E5, F34, G5, F14, F13])), (set([F12, E6, F24, F23]), set([F34, E5, G6, G5, F14, F13])), (set([F12, F24]), set([F23, F34, E6, E5, G6, G5, F14, F13])), (set([E6, F23]), set([F12, F24, F34, E5, G6, G5, F14, F13]))]
Line F16: 
[(set([G1, F45]), set([F23, E1, F25, F24, F35, F34, E6, G6])), (set([G1, F45, E1, F34]), set([F23, F25, F24, F35, E6, G6])), (set([G1, F24, F45, E1, F34]), set([E6, F23, G6, F35, F25])), (set([E6, F23, G6, F35, F25]), set([G1, F24, F45, E1, F34])), (set([E6, F23, G6, F25]), set([F45, E1, G1, F24, F35, F34])), (set([F25, G6]), set([F23, F45, E1, G1, F24, F35, F34, E6])), (set([E6, F23]), set([F45, E1, G1, F25, F24, F35, F34, G6]))]
Line F15: 
[(set([E1, F34]), set([F26, F23, F36, G1, F24, E5, F46, G5])), (set([F24, F46]), set([F26, F23, F36, E1, G1, F34, E5, G5])), (set([F24, F46, E1, F34]), set([F26, F23, F36, G1, E5, G5])), (set([E5, F46, F24, E1, F34]), set([F26, G1, F23, G5, F36])), (set([F26, G1, F23, G5, F36]), set([E5, F46, F24, E1, F34])), (set([F26, F23, G5, F36]), set([E1, G1, F24, F34, E5, F46])), (set([F23, F36]), set([F26, E1, G1, F24, F34, E5, F46, G5])), (set([F26, G5]), set([F23, F36, E1, G1, F24, F34, E5, F46]))]

Type II Trees for (aa2a3a4):

Line E5: 
[(set([G2, F56]), set([F45, G1, F15, G4, G3, F25, F35, G6])), (set([F25, G6]), set([F45, G1, F56, F15, G4, G3, F35, G2])), (set([G1, G4]), set([F45, F56, F15, G3, F25, F35, G2, G6])), (set([F45, F15]), set([G1, F56, G4, G3, F25, F35, G2, G6])), (set([G1, G4, F35]), set([F45, F56, F15, G3, F25, G2, G6])), (set([F45, F15, G3]), set([G1, F56, G4, F25, F35, G2, G6])), (set([G2, F25, F56, G6]), set([F45, G1, F15, G4, G3, F35]))]
Line F35: 
[(set([F26, E3]), set([F12, F16, G3, F24, E5, F46, G5, F14])), (set([G5, F14]), set([F26, F12, F16, G3, F24, E3, E5, F46])), (set([F26, E3, G5, F14]), set([F12, F16, G3, F24, E5, F46])), (set([F12, F24, F46, F16]), set([F26, G3, E3, E5, G5, F14])), (set([F46, F16]), set([F26, F12, G3, F24, E3, E5, G5, F14])), (set([F12, F24]), set([F26, F16, G3, E3, E5, F46, G5, F14]))]
Line G3: 
[(set([E4, E1]), set([F23, F36, E2, F35, F34, E6, E5, F13])), (set([F34, F13]), set([F23, F36, E1, E4, E2, F35, E6, E5])), (set([F34, E4, E1, F13]), set([F23, F36, E2, F35, E6, E5])), (set([E6, F23, F36, E2]), set([E1, E4, F35, F34, E5, F13])), (set([F36, E2]), set([F23, E1, E4, F35, F34, E6, E5, F13])), (set([E6, F23]), set([F36, E1, E4, E2, F35, F34, E5, F13]))]