2026-06-29

Below is the smallest counterexample to the integral OHCP I have found:

Here is the Hasse diagram for $K$:

Code output:

Dimension: 3
Euler Char: 1

c = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; lambda=0
   z*=0.5:  xp[25]=0.5 yp[0]=0.75 yp[1]=0.25 ym[2]=0.75 ym[3]=0.75 yp[4]=0.25 ym[5]=0.5 yp[6]=0.5 ym[7]=1.25 yp[8]=0.25 ym[9]=0.5 yp[10]=1 yp[11]=0.25 ym[12]=0.25 yp[13]=0.75 ym[14]=0.5 ym[15]=0.75 ym[16]=0.25 ym[17]=0.75 yp[18]=1 ym[19]=0.75 ym[20]=0.25 yp[21]=0.25 yp[23]=1 yp[24]=0.5
  
  x = 0.5*[0,5]
  y = 0.75*[3,4,6] + 0.25*[0,4,6] + -0.75*[0,3,6] + -0.75*[0,3,4] + 0.25*[1,4,6] + -0.5*[0,1,6] + 0.5*[0,1,4] + -1.25*[4,6,7] + 0.25*[1,6,7] + -0.5*[1,4,7] + 1*[2,4,7] + 0.25*[1,2,7] + -0.25*[1,2,4] + 0.75*[4,5,7] + -0.5*[2,5,7] + -0.75*[2,4,5] + -0.25*[5,7,8] + -0.75*[2,7,8] + 1*[2,5,8] + -0.75*[3,5,8] + -0.25*[2,3,8] + 0.25*[2,3,5] + 1*[0,3,8] + 0.5*[0,3,5]

Several iterations had $|\det B|\ne 1$ (see below). Of those with $|\det B|\ne 1$, they had the following SNF:

Testing 'mats/B_46.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4]
Testing 'mats/B_62.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_66.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_69.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_51.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6]
Testing 'mats/B_47.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
Testing 'mats/B_57.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6]
Testing 'mats/B_61.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2]
Testing 'mats/B_58.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 8]
Testing 'mats/B_54.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 12]
Testing 'mats/B_45.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4]
Testing 'mats/B_56.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 8]
Testing 'mats/B_41.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2]
Testing 'mats/B_63.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_67.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_70.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4]
Testing 'mats/B_52.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8]
Testing 'mats/B_59.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 6]
Testing 'mats/B_71.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4]
Testing 'mats/B_60.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4]
Testing 'mats/B_42.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2]
Testing 'mats/B_68.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_40.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
Testing 'mats/B_43.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2]
Testing 'mats/B_65.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_44.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2]
Testing 'mats/B_55.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 14]
Testing 'mats/B_50.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
Testing 'mats/B_64.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
Testing 'mats/B_53.txt': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 14]

Full log:

 28: [Feasible][P2][det(B)=1][z=4][E=[3,4,6];L=[4,6]] 0*[3,4,6] 0*[3,6] 0*[3,4] 1*[0,6] 0*[0,4] 0*[0,3] 0*[1,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 29: [Feasible][P2][det(B)=1][z=4][E=[4,6];L=[3,6]] 0*[3,4,6] 0*[4,6] 0*[3,4] 1*[0,6] 0*[0,4] 0*[0,3] 0*[1,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 30: [Feasible][P2][det(B)=1][z=4][E=[0,4,6];L=[0,4]] 0*[3,4,6] 0*[4,6] 0*[3,4] 1*[0,6] 0*[0,4,6] 0*[0,3] 0*[1,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 31: [Feasible][P2][det(B)=1][z=4][E=[0,3,6];L=[0,3]] 0*[3,4,6] 0*[4,6] 0*[3,4] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 32: [Feasible][P2][det(B)=1][z=4][E=[0,3,8];L=[4,6]] 0*[3,4,6] 0*[0,3,8] 0*[3,4] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 33: [Feasible][P2][det(B)=1][z=4][E=[1,4,6];L=[1,6]] 0*[3,4,6] 0*[0,3,8] 0*[3,4] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 34: [Feasible][P2][det(B)=1][z=4][E=[0,1,6];L=[3,4]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,1] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 35: [Feasible][P2][det(B)=1][z=4][E=[0,4];L=[0,1]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,4] 1*[6,7] 0*[4,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 36: [Feasible][P2][det(B)=1][z=4][E=[4,6,7];L=[4,7]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 37: [Feasible][P2][det(B)=1][z=4][E=[1,6,7];L=[1,7]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 38: [Feasible][P2][det(B)=1][z=4][E=[2,4,7];L=[2,7]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,4] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 39: [Feasible][P2][det(B)=1][z=4][E=[1,2,7];L=[1,4]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[2,4] 0*[1,2] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 40: [Feasible][P2][det(B)=2][z=4][E=[0,1,4];L=[1,2]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[2,4] 0*[0,1,4] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 41: [Feasible][P2][det(B)=4][z=4][E=[1,2,4];L=[2,4]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 42: [Feasible][P2][det(B)=4][z=4][E=[4,5,7];L=[5,7]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 43: [Feasible][P2][det(B)=4][z=4][E=[2,5,7];L=[2,5]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 44: [Feasible][P2][det(B)=4][z=4][E=[5,7,8];L=[5,8]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[0,4] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 45: [Feasible][P2][det(B)=8][z=4][E=[2,5,8];L=[0,4]] 0*[3,4,6] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 46: [Feasible][P2][det(B)=8][z=4][E=[3,4];L=[3,4,6]] 0*[3,4] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[1,4,6] 0*[1,2,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 47: [Feasible][P2][det(B)=2][z=4][E=[3,4,6];L=[1,4,6]] 0*[3,4] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[3,4,6] 0*[1,2,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[2,4,7] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 48: [Feasible][P2][det(B)=1][z=4][E=[1,6];L=[2,4,7]] 0*[3,4] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[3,4,6] 0*[1,2,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[1,6] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 49: [Feasible][P2][det(B)=1][z=4][E=[2,4,7];L=[1,2,7]] 0*[3,4] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[3,4,6] 0*[2,4,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[1,6] 0*[1,2,4] 0*[0,1,4] 0*[4,5,7] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 50: [Feasible][P2][det(B)=2][z=4][E=[1,2];L=[4,5,7]] 0*[3,4] 0*[0,3,8] 0*[0,1,6] 1*[0,6] 0*[0,4,6] 0*[0,3,6] 0*[3,4,6] 0*[2,4,7] 0*[2,5,8] 1*[6,7] 0*[4,6,7] 0*[1,6,7] 0*[1,6] 0*[1,2,4] 0*[0,1,4] 0*[1,2] 0*[4,5] 0*[2,5,7] 1*[7,8] 0*[5,7,8] 0*[2,8] 0*[3,8] 0*[3,5] 0*[2,3] 1*[0,8] 0*[0,5]
	 x = 1*[0,6] + 1*[6,7] + 1*[7,8] + -1*[0,8]; y = 
 51: [Feasible][P2][det(B)=6][z=3.83333][E=[4,5,7];L=[0,6]] 0.666667*[3,4] 0.666667*[0,3,8] 0.166667*[0,1,6] 0.333333*[4,5,7] 0.166667*[0,4,6] 0.666667*[0,3,6] 0.666667*[3,4,6] 0.166667*[2,4,7] 0.166667*[2,5,8] 0.5*[6,7] 0.5*[4,6,7] 0*[1,6,7] 0.166667*[1,6] 0.166667*[1,2,4] 0.166667*[0,1,4] 0.166667*[1,2] 0.333333*[4,5] 0.166667*[2,5,7] 0.833333*[7,8] 0.166667*[5,7,8] 0.166667*[2,8] 0.666667*[3,8] 0*[3,5] 0*[2,3] 0.333333*[0,8] 0*[0,5]
	 x = 0.666667*[3,4] + 0.5*[6,7] + 0.333333*[4,5] + 0.833333*[7,8] + 0.166667*[2,8] + 0.666667*[3,8] + -0.166667*[1,6] + -0.166667*[1,2] + -0.333333*[0,8]; y = 0.666667*[3,4,6] + 0.166667*[0,1,4] + 0.166667*[2,4,7] + 0.333333*[4,5,7] + 0.166667*[2,5,8] + 0.666667*[0,3,8] + -0.166667*[0,4,6] + -0.666667*[0,3,6] + -0.166667*[0,1,6] + -0.5*[4,6,7] + -0.166667*[1,2,4] + -0.166667*[2,5,7] + -0.166667*[5,7,8]
 52: [Feasible][P2][det(B)=8][z=3.75][E=[1,4,6];L=[1,6]] 0.75*[3,4] 0.75*[0,3,8] 0.125*[0,1,6] 0.5*[4,5,7] 0.125*[0,4,6] 0.75*[0,3,6] 0.75*[3,4,6] 0.25*[2,4,7] 0.25*[2,5,8] 0.25*[6,7] 0.75*[4,6,7] 0*[1,6,7] 0.125*[1,4,6] 0.25*[1,2,4] 0.125*[0,1,4] 0.25*[1,2] 0.5*[4,5] 0.25*[2,5,7] 0.75*[7,8] 0.25*[5,7,8] 0.25*[2,8] 0.75*[3,8] 0*[3,5] 0*[2,3] 0.25*[0,8] 0*[0,5]
	 x = 0.75*[3,4] + 0.25*[6,7] + 0.5*[4,5] + 0.75*[7,8] + 0.25*[2,8] + 0.75*[3,8] + -0.25*[1,2] + -0.25*[0,8]; y = 0.75*[3,4,6] + 0.125*[1,4,6] + 0.125*[0,1,4] + 0.25*[2,4,7] + 0.5*[4,5,7] + 0.25*[2,5,8] + 0.75*[0,3,8] + -0.125*[0,4,6] + -0.75*[0,3,6] + -0.125*[0,1,6] + -0.75*[4,6,7] + -0.25*[1,2,4] + -0.25*[2,5,7] + -0.25*[5,7,8]
 53: [Feasible][P2][det(B)=28][z=3.71429][E=[1,4,7];L=[6,7]] 0.857143*[3,4] 0.857143*[0,3,8] 0.0714286*[0,1,6] 0.571429*[4,5,7] 0.0714286*[0,4,6] 0.857143*[0,3,6] 0.857143*[3,4,6] 0.285714*[2,4,7] 0.285714*[2,5,8] 0.0714286*[1,4,7] 0.928571*[4,6,7] 0.0714286*[1,6,7] 0.142857*[1,4,6] 0.285714*[1,2,4] 0.0714286*[0,1,4] 0.285714*[1,2] 0.571429*[4,5] 0.285714*[2,5,7] 0.714286*[7,8] 0.285714*[5,7,8] 0.285714*[2,8] 0.857143*[3,8] 0*[3,5] 0*[2,3] 0.142857*[0,8] 0*[0,5]
	 x = 0.857143*[3,4] + 0.571429*[4,5] + 0.714286*[7,8] + 0.285714*[2,8] + 0.857143*[3,8] + -0.285714*[1,2] + -0.142857*[0,8]; y = 0.857143*[3,4,6] + 0.142857*[1,4,6] + 0.0714286*[0,1,4] + 0.0714286*[1,4,7] + 0.285714*[2,4,7] + 0.571429*[4,5,7] + 0.285714*[2,5,8] + 0.857143*[0,3,8] + -0.0714286*[0,4,6] + -0.857143*[0,3,6] + -0.0714286*[0,1,6] + -0.928571*[4,6,7] + -0.0714286*[1,6,7] + -0.285714*[1,2,4] + -0.285714*[2,5,7] + -0.285714*[5,7,8]
 54: [Feasible][P2][det(B)=24][z=3.66667][E=[1,2,7];L=[1,4,7]] 0.833333*[3,4] 0.833333*[0,3,8] 0.0833333*[0,1,6] 0.666667*[4,5,7] 0.0833333*[0,4,6] 0.833333*[0,3,6] 0.833333*[3,4,6] 0.25*[2,4,7] 0.333333*[2,5,8] 0.0833333*[1,2,7] 0.916667*[4,6,7] 0.0833333*[1,6,7] 0.166667*[1,4,6] 0.25*[1,2,4] 0.0833333*[0,1,4] 0.166667*[1,2] 0.666667*[4,5] 0.333333*[2,5,7] 0.666667*[7,8] 0.333333*[5,7,8] 0.333333*[2,8] 0.833333*[3,8] 0*[3,5] 0*[2,3] 0.166667*[0,8] 0*[0,5]
	 x = 0.833333*[3,4] + 0.666667*[4,5] + 0.666667*[7,8] + 0.333333*[2,8] + 0.833333*[3,8] + -0.166667*[1,2] + -0.166667*[0,8]; y = 0.833333*[3,4,6] + 0.166667*[1,4,6] + 0.0833333*[0,1,4] + 0.25*[2,4,7] + 0.0833333*[1,2,7] + 0.666667*[4,5,7] + 0.333333*[2,5,8] + 0.833333*[0,3,8] + -0.0833333*[0,4,6] + -0.833333*[0,3,6] + -0.0833333*[0,1,6] + -0.916667*[4,6,7] + -0.0833333*[1,6,7] + -0.25*[1,2,4] + -0.333333*[2,5,7] + -0.333333*[5,7,8]
 55: [Feasible][P2][det(B)=28][z=3.57143][E=[0,5,8];L=[0,8]] 0.857143*[3,4] 0.857143*[0,3,8] 0.0714286*[0,1,6] 0.714286*[4,5,7] 0.0714286*[0,4,6] 0.857143*[0,3,6] 0.857143*[3,4,6] 0.214286*[2,4,7] 0.285714*[2,5,8] 0.0714286*[1,2,7] 0.928571*[4,6,7] 0.0714286*[1,6,7] 0.142857*[1,4,6] 0.214286*[1,2,4] 0.0714286*[0,1,4] 0.142857*[1,2] 0.714286*[4,5] 0.285714*[2,5,7] 0.571429*[7,8] 0.428571*[5,7,8] 0.285714*[2,8] 0.857143*[3,8] 0*[3,5] 0*[2,3] 0.142857*[0,5,8] 0.142857*[0,5]
	 x = 0.857143*[3,4] + 0.714286*[4,5] + 0.571429*[7,8] + 0.285714*[2,8] + 0.857143*[3,8] + 0.142857*[0,5] + -0.142857*[1,2]; y = 0.857143*[3,4,6] + 0.142857*[1,4,6] + 0.0714286*[0,1,4] + 0.214286*[2,4,7] + 0.0714286*[1,2,7] + 0.714286*[4,5,7] + 0.285714*[2,5,8] + 0.142857*[0,5,8] + 0.857143*[0,3,8] + -0.0714286*[0,4,6] + -0.857143*[0,3,6] + -0.0714286*[0,1,6] + -0.928571*[4,6,7] + -0.0714286*[1,6,7] + -0.214286*[1,2,4] + -0.285714*[2,5,7] + -0.428571*[5,7,8]
 56: [Feasible][P2][det(B)=16][z=3.5][E=[0,6];L=[1,2]] 0.75*[3,4] 0.75*[0,3,8] 0*[0,1,6] 0.75*[4,5,7] 0*[0,4,6] 0.75*[0,3,6] 0.75*[3,4,6] 0.125*[2,4,7] 0.25*[2,5,8] 0.125*[1,2,7] 0.875*[4,6,7] 0.125*[1,6,7] 0.125*[1,4,6] 0.125*[1,2,4] 0*[0,1,4] 0.25*[0,6] 0.75*[4,5] 0.25*[2,5,7] 0.5*[7,8] 0.5*[5,7,8] 0.25*[2,8] 0.75*[3,8] 0*[3,5] 0*[2,3] 0.25*[0,5,8] 0.25*[0,5]
	 x = 0.75*[3,4] + 0.25*[0,6] + 0.75*[4,5] + 0.5*[7,8] + 0.25*[2,8] + 0.75*[3,8] + 0.25*[0,5]; y = 0.75*[3,4,6] + 0.125*[1,4,6] + 0.125*[2,4,7] + 0.125*[1,2,7] + 0.75*[4,5,7] + 0.25*[2,5,8] + 0.25*[0,5,8] + 0.75*[0,3,8] + -0.75*[0,3,6] + -0.875*[4,6,7] + -0.125*[1,6,7] + -0.125*[1,2,4] + -0.25*[2,5,7] + -0.5*[5,7,8]
 57: [Feasible][P2][det(B)=24][z=3][E=[2,7,8];L=[2,8]] 0.666667*[3,4] 0.666667*[0,3,8] 0*[0,1,6] 0.666667*[4,5,7] 0*[0,4,6] 0.666667*[0,3,6] 0.666667*[3,4,6] 0.166667*[2,4,7] 0.166667*[2,5,8] 0.166667*[1,2,7] 0.833333*[4,6,7] 0.166667*[1,6,7] 0.166667*[1,4,6] 0.166667*[1,2,4] 0*[0,1,4] 0.333333*[0,6] 0.666667*[4,5] 0.166667*[2,5,7] 0.333333*[7,8] 0.5*[5,7,8] 0.166667*[2,7,8] 0.666667*[3,8] 0*[3,5] 0*[2,3] 0.333333*[0,5,8] 0.333333*[0,5]
	 x = 0.666667*[3,4] + 0.333333*[0,6] + 0.666667*[4,5] + 0.333333*[7,8] + 0.666667*[3,8] + 0.333333*[0,5]; y = 0.666667*[3,4,6] + 0.166667*[1,4,6] + 0.166667*[2,4,7] + 0.166667*[1,2,7] + 0.666667*[4,5,7] + 0.166667*[2,5,8] + 0.333333*[0,5,8] + 0.666667*[0,3,8] + -0.666667*[0,3,6] + -0.833333*[4,6,7] + -0.166667*[1,6,7] + -0.166667*[1,2,4] + -0.166667*[2,5,7] + -0.5*[5,7,8] + -0.166667*[2,7,8]
 58: [Feasible][P2][det(B)=64][z=2.75][E=[1,4,7];L=[0,6]] 0.75*[3,4] 0.75*[0,3,8] 0.125*[0,1,6] 0.75*[4,5,7] 0.125*[0,4,6] 0.75*[0,3,6] 0.75*[3,4,6] 0.25*[2,4,7] 0.25*[2,5,8] 0.25*[1,2,7] 0.875*[4,6,7] 0.125*[1,6,7] 0.25*[1,4,6] 0.25*[1,2,4] 0.125*[0,1,4] 0.125*[1,4,7] 0.75*[4,5] 0.25*[2,5,7] 0.25*[7,8] 0.5*[5,7,8] 0.25*[2,7,8] 0.75*[3,8] 0*[3,5] 0*[2,3] 0.25*[0,5,8] 0.25*[0,5]
	 x = 0.75*[3,4] + 0.75*[4,5] + 0.25*[7,8] + 0.75*[3,8] + 0.25*[0,5]; y = 0.75*[3,4,6] + 0.25*[1,4,6] + 0.125*[0,1,4] + 0.25*[2,4,7] + 0.25*[1,2,7] + 0.75*[4,5,7] + 0.25*[2,5,8] + 0.25*[0,5,8] + 0.75*[0,3,8] + -0.125*[0,4,6] + -0.75*[0,3,6] + -0.125*[0,1,6] + -0.875*[4,6,7] + -0.125*[1,6,7] + -0.125*[1,4,7] + -0.25*[1,2,4] + -0.25*[2,5,7] + -0.5*[5,7,8] + -0.25*[2,7,8]
 59: [Feasible][P2][det(B)=48][z=2.66667][E=[5,7];L=[7,8]] 0.666667*[3,4] 0.666667*[0,3,8] 0.166667*[0,1,6] 0.666667*[4,5,7] 0.166667*[0,4,6] 0.666667*[0,3,6] 0.666667*[3,4,6] 0.333333*[2,4,7] 0.333333*[2,5,8] 0.333333*[1,2,7] 0.833333*[4,6,7] 0.166667*[1,6,7] 0.333333*[1,4,6] 0.333333*[1,2,4] 0.166667*[0,1,4] 0.166667*[1,4,7] 0.666667*[4,5] 0.333333*[2,5,7] 0.333333*[5,7] 0.666667*[5,7,8] 0.333333*[2,7,8] 0.666667*[3,8] 0*[3,5] 0*[2,3] 0.333333*[0,5,8] 0.333333*[0,5]
	 x = 0.666667*[3,4] + 0.666667*[4,5] + 0.666667*[3,8] + 0.333333*[0,5] + -0.333333*[5,7]; y = 0.666667*[3,4,6] + 0.333333*[1,4,6] + 0.166667*[0,1,4] + 0.333333*[2,4,7] + 0.333333*[1,2,7] + 0.666667*[4,5,7] + 0.333333*[2,5,8] + 0.333333*[0,5,8] + 0.666667*[0,3,8] + -0.166667*[0,4,6] + -0.666667*[0,3,6] + -0.166667*[0,1,6] + -0.833333*[4,6,7] + -0.166667*[1,6,7] + -0.166667*[1,4,7] + -0.333333*[1,2,4] + -0.333333*[2,5,7] + -0.666667*[5,7,8] + -0.333333*[2,7,8]
 60: [Feasible][P2][det(B)=32][z=2.5][E=[0,8];L=[0,5]] 0.5*[3,4] 0.5*[0,3,8] 0.25*[0,1,6] 0.5*[4,5,7] 0.25*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 0.5*[2,4,7] 0.5*[2,5,8] 0.5*[1,2,7] 0.75*[4,6,7] 0.25*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.25*[0,1,4] 0.25*[1,4,7] 0.5*[4,5] 0.5*[2,5,7] 0.5*[5,7] 0.5*[5,7,8] 0.5*[2,7,8] 0.5*[3,8] 0*[3,5] 0*[2,3] 0*[0,5,8] 0.5*[0,8]
	 x = 0.5*[3,4] + 0.5*[4,5] + 0.5*[3,8] + -0.5*[5,7] + -0.5*[0,8]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.25*[0,1,4] + 0.5*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 0.5*[2,5,8] + 0.5*[0,3,8] + -0.25*[0,4,6] + -0.5*[0,3,6] + -0.25*[0,1,6] + -0.75*[4,6,7] + -0.25*[1,6,7] + -0.25*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[5,7,8] + -0.5*[2,7,8]
 61: [Feasible][P2][det(B)=32][z=2][E=[0,3,4];L=[3,4]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 1*[4,5,7] -0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 0.5*[2,4,7] 0.5*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[4,5] 0.5*[2,5,7] 0*[5,7] 0.5*[5,7,8] 0.5*[2,7,8] 1*[3,8] 0*[3,5] 0*[2,3] 0*[0,5,8] 0*[0,8]
	 x = 1*[4,5] + 1*[3,8]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 0.5*[2,4,7] + 0.5*[1,2,7] + 1*[4,5,7] + 0.5*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[5,7,8] + -0.5*[2,7,8]
 62: [Feasible][P2][det(B)=64][z=2][E=[2,4,5];L=[5,7]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 1*[4,5,7] -0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 0.5*[2,4,7] 0.5*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[4,5] 0.5*[2,5,7] 0*[2,4,5] 0.5*[5,7,8] 0.5*[2,7,8] 1*[3,8] 0*[3,5] 0*[2,3] 0*[0,5,8] 0*[0,8]
	 x = 1*[4,5] + 1*[3,8]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 0.5*[2,4,7] + 0.5*[1,2,7] + 1*[4,5,7] + 0.5*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[5,7,8] + -0.5*[2,7,8]
 63: [Feasible][P2][det(B)=64][z=2][E=[3,5,8];L=[3,5]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 1*[4,5,7] 0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 0.5*[2,4,7] 0.5*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[4,5] 0.5*[2,5,7] 0*[2,4,5] 0.5*[5,7,8] 0.5*[2,7,8] 1*[3,8] 0*[3,5,8] 0*[2,3] 0*[0,5,8] 0*[0,8]
	 x = 1*[4,5] + 1*[3,8]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 0.5*[2,4,7] + 0.5*[1,2,7] + 1*[4,5,7] + 0.5*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[5,7,8] + -0.5*[2,7,8]
 64: [Feasible][P2][det(B)=64][z=1][E=[3,5];L=[4,5]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3] 0*[0,5,8] 0*[0,8]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 65: [Feasible][P2][det(B)=64][z=1][E=[2,3,8];L=[2,3]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3,8] 0*[0,5,8] 0*[0,8]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 66: [Feasible][P2][det(B)=128][z=1][E=[2,3,5];L=[0,8]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3,8] 0*[0,5,8] 0*[2,3,5]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 67: [Feasible][P2][det(B)=128][z=1][E=[0,3,5];L=[0,5,8]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,4,6] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3,8] 0*[0,3,5] 0*[2,3,5]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 68: [Feasible][P2][det(B)=64][z=1][E=[0,5];L=[0,4,6]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,5] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[1,6,7] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3,8] 0*[0,3,5] 0*[2,3,5]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 69: [Feasible][P2][det(B)=64][z=1][E=[0,4,6];L=[1,6,7]] 0.5*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.5*[4,5,7] 0*[0,5] 0.5*[0,3,6] 0.5*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.5*[1,2,7] 1*[4,6,7] 0*[0,4,6] 0.5*[1,4,6] 0.5*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 1*[3,5] 0.5*[2,5,7] 0.5*[2,4,5] 0*[5,7,8] 1*[2,7,8] 0*[3,8] 1*[3,5,8] 0*[2,3,8] 0*[0,3,5] 0*[2,3,5]
	 x = -1*[3,5]; y = 0.5*[3,4,6] + 0.5*[1,4,6] + 0.5*[0,1,4] + 1*[2,4,7] + 0.5*[1,2,7] + 0.5*[4,5,7] + 1*[2,5,8] + 1*[0,3,8] + -0.5*[0,3,6] + -0.5*[0,3,4] + -0.5*[0,1,6] + -1*[4,6,7] + -0.5*[1,4,7] + -0.5*[1,2,4] + -0.5*[2,5,7] + -0.5*[2,4,5] + -1*[2,7,8] + -1*[3,5,8]
 70: [Feasible][P2][det(B)=256][z=0.5][E=[1,6,7];L=[3,5]] 0.75*[0,3,4] 1*[0,3,8] 0.5*[0,1,6] 0.75*[4,5,7] 0.5*[0,5] 0.75*[0,3,6] 0.75*[3,4,6] 1*[2,4,7] 1*[2,5,8] 0.25*[1,2,7] 1.25*[4,6,7] 0.25*[0,4,6] 0.25*[1,4,6] 0.25*[1,2,4] 0.5*[0,1,4] 0.5*[1,4,7] 0.25*[1,6,7] 0.5*[2,5,7] 0.75*[2,4,5] 0.25*[5,7,8] 0.75*[2,7,8] 0*[3,8] 0.75*[3,5,8] 0.25*[2,3,8] 0.5*[0,3,5] 0.25*[2,3,5]
	 x = 0.5*[0,5]; y = 0.75*[3,4,6] + 0.25*[0,4,6] + 0.25*[1,4,6] + 0.5*[0,1,4] + 0.25*[1,6,7] + 1*[2,4,7] + 0.25*[1,2,7] + 0.75*[4,5,7] + 1*[2,5,8] + 0.25*[2,3,5] + 1*[0,3,8] + 0.5*[0,3,5] + -0.75*[0,3,6] + -0.75*[0,3,4] + -0.5*[0,1,6] + -1.25*[4,6,7] + -0.5*[1,4,7] + -0.25*[1,2,4] + -0.5*[2,5,7] + -0.75*[2,4,5] + -0.25*[5,7,8] + -0.75*[2,7,8] + -0.75*[3,5,8] + -0.25*[2,3,8]