rep1      2h=(-2, -2, -1, 0, -1, 1, 0, -1) |orbit|=24 level1=['-1/4', '-1/8', '-1/8'] classes=[[0], [1, 2]] cubic hat h(123)=1/4
    flip class [1]: level1=['1/4', '-1/8', '-1/8'] -> orbit rep9  (classes kept: equivalent)
    flip class [2, 3]: level1=['-1/4', '1/8', '1/8'] -> orbit rep9  (classes kept: equivalent)
rep2      2h=(-2, -2, -1, 0, 1, -2, -1, -1) |orbit|=24 level1=['-1/8', '-1/8', '1/8'] classes=[[0, 1], [2]] cubic hat h(123)=-1/8
    flip class [1, 2]: level1=['1/8', '1/8', '1/8'] -> orbit A12 (g0)  (classes merge: only h trivial => h^K trivial)
    flip class [3]: level1=['-1/8', '-1/8', '-1/8'] -> orbit A12 (g0)  (classes merge: only h trivial => h^K trivial)
rep3      2h=(-2, -2, -1, 1, 0, -1, -1, 0) |orbit|=24 level1=['-1/8', '-1/4', '-1/8'] classes=[[0, 2], [1]] cubic hat h(123)=0
    flip class [1, 3]: level1=['1/8', '-1/4', '1/8'] -> orbit rep8  (classes kept: equivalent)
    flip class [2]: level1=['-1/8', '1/4', '-1/8'] -> orbit rep8  (classes kept: equivalent)
A24 (g1)  2h=(-2, -2, -1, 1, 0, 0, -1, -1) |orbit|=24 level1=['-1/8', '-1/8', '-1/8'] classes=[[0, 1, 2]] cubic hat h(123)=1/8
rep5      2h=(-2, -1, -1, 0, 1, -2, 0, -1) |orbit|=24 level1=['-1/8', '-1/8', '1/8'] classes=[[0, 1], [2]] cubic hat h(123)=-1/8
    flip class [1, 2]: level1=['1/8', '1/8', '1/8'] -> orbit D12 (g2)  (classes merge: only h trivial => h^K trivial)
    flip class [3]: level1=['-1/8', '-1/8', '-1/8'] -> orbit D12 (g2)  (classes merge: only h trivial => h^K trivial)
rep6      2h=(-2, -1, 0, -1, 1, -2, -1, 0) |orbit|=24 level1=['-1/8', '-1/8', '1/8'] classes=[[0, 1], [2]] cubic hat h(123)=-3/8
    flip class [1, 2]: level1=['1/8', '1/8', '1/8'] -> orbit C12  (classes merge: only h trivial => h^K trivial)
    flip class [3]: level1=['-1/8', '-1/8', '-1/8'] -> orbit C12  (classes merge: only h trivial => h^K trivial)
rep7      2h=(-1, -2, -1, 0, 1, -2, -1, 0) |orbit|=24 level1=['-1/8', '-1/8', '1/8'] classes=[[0, 1], [2]] cubic hat h(123)=-1/8
    flip class [1, 2]: level1=['1/8', '1/8', '1/8'] -> orbit A24 (g1)  (classes merge: only h trivial => h^K trivial)
    flip class [3]: level1=['-1/8', '-1/8', '-1/8'] -> orbit A24 (g1)  (classes merge: only h trivial => h^K trivial)
rep8      2h=(-1, -2, -1, 0, 1, -2, 0, -1) |orbit|=24 level1=['-1/8', '-1/8', '1/4'] classes=[[0, 1], [2]] cubic hat h(123)=0
    flip class [1, 2]: level1=['1/8', '1/8', '1/4'] -> orbit rep3  (classes kept: equivalent)
    flip class [3]: level1=['-1/8', '-1/8', '-1/4'] -> orbit rep3  (classes kept: equivalent)
rep9      2h=(-1, -2, 0, -1, 1, -2, -1, 0) |orbit|=24 level1=['-1/8', '-1/8', '1/4'] classes=[[0, 1], [2]] cubic hat h(123)=-1/4
    flip class [1, 2]: level1=['1/8', '1/8', '1/4'] -> orbit rep1  (classes kept: equivalent)
    flip class [3]: level1=['-1/8', '-1/8', '-1/4'] -> orbit rep1  (classes kept: equivalent)
rep10     2h=(-1, -2, 0, 0, 1, -1, -1, 0) |orbit|=24 level1=['-1/8', '-1/8', '1/8'] classes=[[0, 1], [2]] cubic hat h(123)=-1/8
    flip class [1, 2]: level1=['1/8', '1/8', '1/8'] -> orbit B12  (classes merge: only h trivial => h^K trivial)
    flip class [3]: level1=['-1/8', '-1/8', '-1/8'] -> orbit B12  (classes merge: only h trivial => h^K trivial)
A12 (g0)  2h=(-2, -2, -2, 1, 0, -1, -1, -1) |orbit|=12 level1=['-1/8', '-1/8', '-1/8'] classes=[[0, 1, 2]] cubic hat h(123)=1/8
B12       2h=(-2, -1, -1, 1, 0, 0, 0, -1) |orbit|=12 level1=['-1/8', '-1/8', '-1/8'] classes=[[0, 1, 2]] cubic hat h(123)=1/8
C12       2h=(-1, -2, -2, 1, -1, 0, 0, -1) |orbit|=12 level1=['-1/8', '-1/8', '-1/8'] classes=[[0, 1, 2]] cubic hat h(123)=3/8
D12 (g2)  2h=(-1, -2, -2, 1, 0, -1, -1, 0) |orbit|=12 level1=['-1/8', '-1/8', '-1/8'] classes=[[0, 1, 2]] cubic hat h(123)=1/8
