old system 0
{2,6,8}{3,4,9}{0,5,10,1,7}
{2,5,9}{3,7,8}{0,6,1,4,10}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,7,9}{3,6,10}
{0,4,6,9}{1,3,5,8}{2,7,10}
is isomorphic to new system 8
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,6}{1,4,8}{2,7,9,5,10}
{0,5,1,7}{4,6,8,10}{2,3,9}
{0,8,3,10}{2,4,7,5}{1,6,9}
{1,3,7,10}{2,6,5,8}{0,4,9}
  0  1  2  3  4  5  6  7  8  9 10
 10  7  3  1  8  5  6  2  0  4  9
r0->r1 r1->r0 r2->r4 r3->r3 r4->r2 
[c1->c1,c2->c2,c3->c3,c1:012->120,c2:012->021,c3:01234->4321]
[c1->c2,c2->c1,c3->c3,c1:012->021,c2:012->120,c3:01234->4012]
[c1->c1,c2->c2,c3->c3,c1:0123->3210,c2:0123->3210,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->3210,c2:0123->2301,c3:012->012]
[c1->c2,c2->c1,c3->c3,c1:0123->3210,c2:0123->3210,c3:012->102]